Judging by the way you're phrasing the question, it doesn't sound like you're being very mature. For example, you're complaining that it is embarrassing and that you're the life of the party. Though those may be true, you have to give her reasons to trust you. And, you have to explain that it is a part of American culture. I can imagine it being very difficult for her to see "the point" of this.
Some things I would recommend are:
-Suggesting she speaks to the girl's parents whose house you want to sleepover. Since you are in their care for the night, she will need to trust them with your life - as crazy as that may sound. Ask her to talk to them and make sure they are responsible, etc.
-Point out examples of how you are trustworthy. For example, do you get good grades? Do chores? If so, bring those points up. Tell her how you have taken on more responsibility - so you should receive some more freedom(s)
-Explain why it is important to you.
-Explain how it is a part of this culture, just as you are now. And discuss what things may have been a part of her culture that are absent here. Maybe she will understand where you are coming from if you can think of a Bulgarian tradition that might not be popular/heard of here.
-Talk about your independence. And how this can help you achieve more independence and confidence. Being given the trust, freedom, and responsibility of staying away from home for a night is something that can help strengthen adaptability and lessen anxiety about taking on larger tasks (for example, if you had to switch schools in the middle of high school). Being exposed to situations helps people grow - including your mom, in that she will better understand her daughter (you) and work on her own fear of letting you go -- even if only for one night.
Last but not least - when you are given freedom, don't take advantage of it! If you seem spoiled or like you do not appreciate something, this isn't more likely to convince your parents of trusting or rewarding you. If you are given a time you have to be home by, then be home. If they want you to call them, don't forget to call. Don't do stupid things once you're there. Be glad your mom trusted you and pay her back by respecting your friend's house & family and having fun that doesn't result in you getting in trouble. :)