If you are currently living in New York then I think that is where you need to apply. I can't see any logic in travelling back to Bulgaria just to make an application there, and indeed as the general rule is that you need to make the application where you are normally living at the time. So it is conceivable that the British Embassy in Bulgaria may even decline to deal with the application, or would refer it to New York (causing a long delay).
But can I ask, how long have you been living in the States?
How to complete the form VAF1? You will appreciate that the form attempts to deal with a number of different situations, not just an EEA Family Permit. You refer to Section 6 of the form. I think ... if in doubt .. .answer the questions honestly, even if it does not appear logical to do so. You will see that there are sections of the form, such as Sections 7, 8 and 9, that will not need to be completed by you. I agree that logically Section 6 does not appear too relevant to you but as the designer of the form seems to want it completed by everyone, I think you need to do so.
However, Section 10! That provides a great chance for you to explain that the employment mentioned in Section 6 will of course be ended shortly before you move to the UK.
Of course if you have given up the employment when you apply, say that in Section 6. Don't just leave the section totally blank.
Working as a waiter a minus point? Certainly not. But again, why not use Section 10 as an opportunity to give details of your Degree?
Finally, it would be wrong to think of the issue of an EEA Family Permit as a total formality, but really it is one of the easiest applications to make. On proving your family relationship with an EEA National, and assuming you have not disclosed horrendous criminal convictions in Section 4 of the form, the permit will be issued! It is not a question of you needing to prove that you will be able to get a wonderful job and earn lots of money, or anything like that. It is as simple as :-
- your wife as an EEA Citizen having the right to live and work in the UK (to work subject only to her simply registering that fact)
- your as a non-EEA citizen being her Family Member, you have the right to live with her, and accordingly the same rights as her
The only difference is that whilst your wife's passport proves her rights, you need an EEA Family Permit in your Bulgarian passport in order to prove your right to be with her.