Dear, in these situations it is best to have the facts BEFORE accusing someone, however, these things happen.
Well....perhaps find a nice card and write a nice note telling her how bad you feel about what happened and express that you truly value her as a friend and you miss her terribly. Send it and she what happens; wait for her to respond.
If you are truly friends you two will get past this. This is nothing that can't be repaired.
Hi there. Well, you obviously hurt her feelings. You basically told her that you think she is the kind of person that would be so disloyal to you that she'd interfere with your boyfriend and send emails. That is saying you don't think very highly of her. it would hurt, for sure.
I think that you give her time to get over it. Accusing someone of something when they are innocent feels rotten. she's feeling rotten and now is second guessing you right back.
I do think time will heal this. Send her a note or letter telling her how much you miss her, value your friendship, and are sorry for ever doubting her. And tell her that you will always be there to be her friend.
Then kiss her butt for a while. and hopefully it will blow over. good luck dear