I've transferred a .EU domain and it's really easy to do so.
1: Ask internet.bs to let them do a transfer, this means you will have to apply for the domains in the regular fashion you would also do when they where freely available.
2: You will recieve a email from Eurid with a confirmation request. This will contain a link to the official site of Eurid. Upon clicking the link you will notice that the confirmation request is waiting for you. You merely have to go through a couple of questions, Yes or No.
3: Now you need to wait a few days for the ownership transfer to complete.
---------------------------------------------------------------------------
I did not requested the transfer myself, i got an email in my inbox from Eurid asking for the confirmation of transfer of ownership when i sold a .EU domain.
So the buyer had apperently requested the transfer from his/her's registrar.
No need for control panel procedures, everything is done through Eurid themself.
Apply for the same domain with internet.bs and you will recieve a confirmation email for the transfer. You will see the current owner information and next to it you will see the new owner information and you will be asked to comply or not to if you do not want to. In your case you will see the same information apart from the registrar the domain is being transferred.
And the transfer is free! In my experience that is, if you have to pay for it then it's your current registrar where your domain(s) is/are residing. Eurid themself do not charge any transfer fees.
Hope that helped.