don't worry about that. some girls have a bit of bleeding but it's much more like light spotting than an all-out heavy day period type of bleeding.
one thing you can do is to put a towel under your bottom the first time you do it in case you're concerned about getting a little bit of blood on the sheets.
since he knows it's your first time, tell him to go super easy on you and also to expect that there may be some bleeding. other than that, no worries.
it shouldn't be embarrassing to you. this is nature taking place. sex is not always "pretty"...sometimes it is sweaty and earthy and natural...it's passionate.
sometimes people do unpredictable things during sex...someone really quiet may become loud, or someone loud may become very quiet...the variable list goes on forever. sometimes it's pretty clean and sometimes its messy. but God gave us the equipment we have so we could ENJOY sex.
enjoy your sex life (including your first experience). have fun at it...make it special, take your time (both of you) and just enjoy it. don't get caught up in the little stuff like a few drops of blood. mainly, you need to relax. relax.
let me know if i can help you. good luck
jasmine