Yes you can. Starting from May 8, 2013 every EU citizen can enter to Kosovo with ID card only, as mentioned on the Kosovo Ministry of Foreign Affairs website (at the bottom of the page)
According to the Bulgarian Ministry of Foreign Affairs, as a Bulgarian citizen you need a valid Bulgarian passport to enter Kosovo.
For citizens from other EU countries it is analogical. They need a valid passport of their home country. I have checked the sites of several ministries of foreign affairs. They all say the same thing.
P.S. This information might be relevant too, although it is not directly linked to your question.
Kosovo has not yet defined a particular policy on this topic.
According to its Ministry of Foreign Affairs, there is no distinction based on the citizenship. Every citizen may therefore enter the country and stay for a maximum of 90 days. However, there are some rules to respect. You should be able to :
After 90 days, a traveller must contact the Kosovo police to be registered, but it is unclear if the right to stay will be granted.
EDIT : See @Janusz answer, as the policy is now defined and EU citizens can enter with an ID card.
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