I feel very sorry for you, this is a very scary situation, for any rider, confident, novice and all in between.
I haven't read all the posts from people, so I'm sorry if I'm repeating ideas (sorry I know it's kinda rude not to read everyone's, I do apologise)
What I would do, is try and get in touch with the seller. Ask them if they were aware of it (and they probably were, but will probably deny it) tell them the problem, ask if they know why she's doing it. Tell them you're very upset that she was sold as a novice horse when she clearly is not (even if they deny knowing about the rearing, still voice that you're very upset)
Get the horse insured for 3rd party, I know it will cost, but it'll cost a lot more if she does damage.
Don't take her out riding, walk her out, preferably to the bmx place and keep her at a distance where she is comfortable (or just a little uncomfortable - head up, looking a little worried but not rearing) Praise her, tell her she's the most brilliant horse in the world, feed her treats (I know not everyone gives treats but I would in this situation), rub her neck make her feel generally comfortable, then take her home the moment she shows signs of relaxing - dropping her head, licking and chewing, one big sigh/snort out of air.
The next time, take her to the same point, make her feel good, and then walk her a few steps closer (still leading by the way, not riding), again, make her feel comfortable, praise, rubs Etc.
Each time, go to the same place, and once she is settled there, go forward until she settles, forward again. It will take a very long time, but it is the only thing I could come up with that is fairly safe (as safe as possible with a rearer)
Also, ask your bmx friend to bring his bike to where you keep her. If he's willing (if not, get an old bike no one cares for) put it on the ground, let her sniff it, like it, chew it, paw at it. Then stand it up, let her do the same (if she knocks it over, she might spook, fair enough, just pick it up again, and let her have another go, let her keep knocking it until it doesn't bother her any more) Then get your bmx-er friend to cycle around, at a distance. Let her watch (keep her on a lead rope for this) let him cycle round, and then take her to a point a bit closer, make her feel comfortable, then a bit closer and keep repeating until she's really close but relaxed. It may take several sessions.
I'm not sure how you could desensitise her to motorbikes unless you know anyone with one. I hope this might help...
If you don't feel comfortable with a horse, don't risk your or anyone's life. Only do it if you feel you could cope. If you sell this horse, tell the new owner she is good to be ridden (if she is) in the school or in the field, but does need road work, tell them that she is very uncomfortable with bikes. I hope you're okay, it is a terrible situation, for any rider.
Last edited by HollyLolly; 10-16-2012 at 05:18 PM.