hi pnwright,
the logistic regression with categorical IVs will do something quite close to what you are interested in, if I understand correctly. It will create indicator variables for the categories you have, define one as a base and compare the outcome of each of the other categories to the outcome of the base variable you picked.
To make it concrete, imagine that you have 4 bait types, rabbit, chicken, lamb .. etc. When you do this type of analysis you will pick one bait type as the basis, say meat. The logistic regression model will give you an estimate of the ratio of odds of seeing an animal in the trap with meat as a bait and the odds of seeing an animal with chicken as a bait.. and so on for each type of bait. It does not compare each bait type to each but all of them to the one you picked as a base,
From the odds ratios you can go to an estimate of the probailities and get the probability of seeing an animal in the trap for each bait type.
regards
rogojel