Avoiding rabbit cross-contamination

We had some devastating tornadoes roll through here about a month ago, and afterwards I found a bunny in my yard. I caught her and brought her inside to safety and registered her with all of the lost and found pet lists. As the humane society was overwhelmed after the storms and I have hay and toys to spare, I offered to foster her in my thankfully unaffected home.

I also have one very spoiled boy chinchilla. Thankfully, instinct kicked in and I remembered that chins and bunnies should not be kept together for some reason (now I remember - pasturella). The bunny is housed in a separate room, and I shower and change clothes between animals. Is that enough to prevent the spread of disease?

For the first two weeks, the bunny was very skittish and barely moved from the box in her pen. Now that she is more comfortable in my home, I would like to give her some out-of-pen exercise. I have a huge chin-proofed area for my boy. I would love for the bunny to be able to use this area, but I am concerned about the transmission of disease (also is there any way to have her tested to see if she carries it?). Does pasturella survive outside the body? If so, would steam mopping between animals kill it? Or would I be better off bunny-proofing a smaller area for her? The absolute last thing I want to do is expose my boy to a potentially deadly disease.