score:2
1.She has a bank account in Tbilisi, but am not sure the funds will be enough for the trip to the UK. I am looking to transfer some money from my account to hers that can help her with the Visa. Please advice if this is a good idea.
If you do that, make sure to explicitly declare in a letter that it is a gift from you, or she could well be refused. Transferring a high amount of money to the applicant "to help with the visa" is frequently interpreted as what we call funds parking, a common cause for refusal.
Having enough money at one point in time is not enough: they want to see that she regularly gets a steady amount of income, and that that money is enough for her to visit the UK without throwing away her life savings. The only acceptable proof is several consecutive bank statements showing a steady and sufficient income
2.Can I sponsor her entire trip? I am paying for her flights and the accommodation is covered as she is staying with me. I have a studio living in a student accommodation. The problem here is I have just come to the UK and only opened a bank account yesterday.
Your circumstances make you (bluntly speaking) a worthless sponsor, as a sponsor is expected to be well-established in the UK and have a steady income there allowing them to financially support a visitor from abroad and be able to prove it through multiple consecutive bank statements.
Will UKBA accept such a short period bank statement? I have more than enough funds to provide for the both of us on her trip here btw.
If they can't see through at least 5 or 6 consecutive bank statements that you have a steady income that's sufficient to support a visitor from abroad, they're not going to accept your sponsorship.
What this means is: unless your girlfriend's funds are clearly enough to support herself whilst in the UK, she should cancel her plans to come to the UK, as the risks are too high.
Once she gets a stable income that's high enough for her to be able to afford a trip to the UK without working there, she can apply.