The bath room in our Casita
is small enough that I don't think it would work for us to have a shower curtain installed to keep the toilet area dry. Not enough elbow room for it. Because the shower water tends to pond in one of the corners behind the toilet area (which is higher than the shower floor), I keep a big sponge behind the bathroom sink and scootch the water forward, so it will go down the shower drain. I also do a quick wipe-down on the shower walls, the toilet lid, etc. Then, unless it's very, very cold outside, I leave the shower window open. (Newer Casitas have a vent fan in the bathroom, which may make the window thing unnecessary. I don't know.)
I also don't know how similar the Escape
bathroom is to the ones that Casita
uses. If your trailer's "throne" area is installed where the water will drain off it, instead of ponding in the corner, I'd say either a sponge or a chamois-cloth, like Alf suggests, will be fine for the job.
Congrats on your new trailer!