Can Bulgarian citizen travel to Ireland with only their national ID card?

TL:DR TL:DR What doesnt change- passport is always accepted.

TL:DR From 1 October 2021, EU nationals will have to show a valid passport when entering Northern Ireland. Always check what form of ID is required by your individual airline, ferry company or travel agent before traveling.
So even if before was possible also with just id, then when it has few time changed, but airlines might still require passport even if country allows just id.

If you are not a citizen of an EEA member state (The EU plus Iceland, Norway and Liechtenstein), you may need a visa to travel to Ireland, even if you have a Schengen visa.

For visa holder (not citizen, resident permit is not citizen, but acts as visa, also national id is ment as identity card of nation not as nationality but as a place not a person having nationality, so dont mix up english language barrier)– yes, take your countries passport (as in anyone always takes, because id is not a travel document, just national identification to where you can currently belong), because your staying permission isnt citizen, but as visa to travel to shengen, but when traveling with visa you need your passport, and also traveling more then 1 country (you want to travel from Amsterdam) you need:

Passport and visa requirements
If you are a non-EU national wishing to visit or travel within the EU, you will need a passport:

valid for at least 3 months after the date you intend to leave the EU country you are visiting,
which was issued within the previous 10 years,
and possibly a visa. You should apply for a visa from the consulate or embassy of the country you are visiting. If your visa is from a Schengen area country, it automatically allows you to travel to the other Schengen countries as well. If you have a valid residence permit from one of those Schengen countries, it is equivalent to a visa. You may need a national visa to visit non-Schengen countries.

Border officials in EU countries may ask for other supporting documents such as an invitation letter, proof of lodging, return or round-trip ticket. For the precise requirements contact the local consular services of the EU country in question.

There are a number of countries whose nationals do not need a visa to visit the EU for three months or less. The list of countries whose nationals require visas to travel to Ireland differs slightly from other EU countries.

Warning
Entry conditions to Ireland are based on national law and differ from EU rules.

So since you live mostly in Bulgaria, then you applied for visa (resident permit on some basis) because:

Where do I apply for a Schengen visa?
You only need to make one visa application for your visit, even if you plan to travel to more than one country in the Schengen Area. There are rules about which country’s embassy you should make your visa application to:

If you are visiting one country in the Schengen Area, you should apply to the embassy of the country you plan to visit
If you are visiting more than one country, you should make your application to the embassy of the country where you plan to spend the most time
If you are spending the same amount of time in more than one country, you should apply to the embassy of the country where you are going first.

Border officials in EU countries may ask for other supporting documents such as an invitation letter, proof of lodging, return or round-trip ticket. For the precise requirements contact the local consular services of the EU country in question.

There are a number of countries whose nationals do not need a visa to visit the EU for three months or less. The list of countries whose nationals require visas to travel to Ireland differs slightly from other EU countries.

Long answer for citizens, that want to try travel only with id and in Ireland:

Passengers arriving in Ireland from countries need to self-isolate for 14 days.
Right now any movement is spreading virus. So need to do full quarantine, but problems happened since some people dont stop the virus https://virusstop.org/ and walk around, not knowing 2 days that they spreading without symptoms, since some viruses dont have sympotms until 3rd day. So 14 days wont be able to walk around without police observation.
https://reopen.europa.eu/en

https://www.citizensinformation.ie/en/moving_country/moving_to_ireland/coming_to_live_in_ireland/permission_to_land_in_ireland.html

Ireland is not part of the Schengen Area. This means that you must have a national passport or national identity card to enter Ireland from the EEA.

EEA, UK and Swiss nationals and permission to enter Ireland
EEA, and Swiss citizens have the right to move freely in the EEA, and you can only be refused permission to enter Ireland in very limited situations:

You are suffering from a serious contagious disease which poses a serious threat to the population
Your past behaviour, including any criminal convictions you may have, is deemed to pose a substantial risk to public security or public policy.

If by road then would cross England.

This should be checked not on internet forum, since info can change, but to be sure in your country and all countries you will be traveling thrue, but better is allways to have passport and wont have to think about risks. Also because if loosing one, then will have other. Also never know if wont fly to another country with some new travel plans where you need a passport.

Here example how info changed about theese national id cards ment for inside usage.

1st national id cards some countrys allowed to vote some not.

2nd some countrys accepted some country id cards.

3rd some countries not allowing to fly in at all, like for high risks have changed. https://www.schengenvisainfo.com/news/bulgaria-brings-back-entry-ban-on-travel-from-us-upon-eu-councils-recommendation/

4th some countrys not accepting anymore some country id and in this case if with car will be traveling thrue such country https://www.independent.co.uk/travel/news-and-advice/european-union-id-cards-brexit-passports-b1930474.html .

What has changed?
More than 200 million Europeans can no longer visit the UK – unless they get passports. The government says: “You will not be able to use an EU, EEA or Swiss national ID card to enter the UK from 1 October 2021”.

Any exceptions?
Until the end of 2025 there will be a few exemptions, notably for people who have “settled or pre-settled status under the EU Settlement Scheme”, or those who have applied to it or have an EU Settlement Scheme family permit.

So in this case not to risk. I would not say to risk and go only with id card.

Bulgaria is not in Schengen zone. Id is not passport. Countries started accepting national id, but is not still real document. Its currently experiment, to make people have some id to not waste time checking id in police.

You should not lose your passport or give it or sell it. Keep it to get back home. Dont risk. ID is just smaller identification, but not a passport.
Easy google shows recomendation https://europa.eu/youreurope/citizens/travel/entry-exit/eu-citizen/index_en.htm –

Even if you don’t need a passport for border checks within the Schengen area , it is still always highly recommended to take a passport or ID card with you, so you can prove your identity if needed (if stopped by police, boarding a plane, etc.). Schengen EU countries have the possibility of adopting national rules obliging you to hold or carry papers and documents when you are present on their territory.

Driving licences, post, bank or tax cards are not accepted as valid travel documents or proof of identity.

Yes, an EU ID card can be used for entry to any EU member state, including Ireland.

The only likely complication would be if you’re going via the UK. Connections to Ireland are treated as domestic connections in the UK so you’d have to pass UK border control for which you would need a passport.