In reply to Mountain Spirit:
I would agree that small group lessons are fine, especially if you are fairly new to skiing (as someone else said, I left the private lessons until I had been skiing for 4 or 5 years and was looking to solve particular problems like skiing bumps - then I only did one in a week, as they are expensive) and the social aspect of group lessons is great.
You will probably find that Neilson have an arrangement with one specific ski school and send all their clients there. They will be able to arrange group or private lessons for you with that school, but probably won't send you elsewhere.
If you want very small groups, it might be worth searching on the web for the ski schools in your resort and find one that offers what you are looking for (i.e. guaranteed small group sizes). You can then book with them for yourself before you go. Most ski schools do seem to be much of a muchness for beginner/early stage group lessons though.
With most group lessons that aren't for absolute beginners, they will often make you do a run or two of the nursery slope so they can assess you and then split you into smaller groups by ability - if you are right at the top or bottom of your group, you might find yourself moved to another group that fits your abilities better later in the week.
I can't offer any specific recommendations for your resort in Bulgaria though.