I'm not very good at it either, so you know what I did?
I told the jazz director that. Outright, I said during the audition, "I'm not so great at sight reading, and I really don't know anything about improv, so sorry if I'm a disgrace." Granted, my director is a very understanding person, and really really wanted me to join jazz band...
Sightreading wasn't part of the audition, so I didn't have to really worry about it right then and there, but he was supposed to test me a bit on improv. What he did instead was some call and response: he played a few notes on a vibraphone, I played them back. Simple stuff.
A little advice on sight reading: A good musician listens just as much as he plays. Start listening to a lot of jazz, study people's solos, and when it comes time to sightread during practice, surrounded by kiddos who have been doing this kind of thing for years, listen to them while you play. This may just have been coincidence, but it seems that there were a lot of repeated rhythms in the different charts we played during our first practice. If that's the case for you, you'll start to recognize the rhythms and etc, and it'll become a little easier.
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