If you know that he loves and respects you.
If you know that he never hangs out with her alone.
If you know that he would drop the friendship if you are that neurotic about it.
If you know all those things then why are you being a ninny?
He is respecting you, the relationship, your feelings and he's not doing anything to cross monogamous relationship boundaries so what is the problem?
You can get past this by doing the mental work YOU need to do to actually trust your boyfriend rather then just give it lip service. I'm sorry I'm being straight up but I guess I'm having a hard time understanding your insecurity when you've not been given any reason to be insecure and therefor its you that needs to do the work to make yourself more comfortable rather then force him to give up a friend that he doesn't cross platonic friendship boundaries on her nor does he cross romantic relationship boundaries on you.
Now... if he was spending one on one time with her, doing date like activities with her without you present, was spending copious amount of time with her on the phone/texting/emailing and ignoring you while he did it, if he was sending her letters that he also said the same thing to you in, if he was crossing monogamous relationship boundaries on you ~ Then yes, I'd be on your side 100%.
As he's not doing anything for you to worry about then how about you don't worry and just enjoy your boyfriend and the value (he shows you in actions) that he has for you.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion