The best way that I can think of is to try to earn your mom's trust. Let her know that you are mature enough to deal with this. Start by explaining to her how important this is to you. Maybe this can best be done in a letter so that it doesn't set off an argument immediately. Ask her what her fears are about you dating and try to address them. It can take awhile to earn her trust, but persistence pays off (and this is very different from nagging.)
Explain to her that there's a boy you are interested in, and can he come over and watch a movie while your mom's there? Try to start small. Maybe by the time you are 16 she'll let you go on "group dates" where you are with a mixed group of friends and not just alone with a guy. Take whatever chance she gives you to prove your trust. Sneaking around behind her back or doing more than she limits is not a way to gain trust. If she catches you it will only increase her worries and fears.