In reply to Reach>Talent: Well, rest it
That is the only thing that works with tendon injuries. However, you are going ice climbing in 2 weeks, I would:
Forget about strength training. One week of total rest, dont use the bicep any more than necessary. Second week do some gentle stretching after a hot shower to warm the muscles. When you go climbing, strap up just above and below your elbow with some stretchy tape. This will take as much pressure off your bicep tendon as possible. However, in the long run, youre still going to be stressing it, its just a matter of minimising the damage (if it really is bicep tendonitis)