Give them a crock or something deep enough to bathe in with a lip or edge they can perch on. That way they can bathe as they see fit. I wouldn't leave it in there but giving them the opportunity is good.
Keep them away from drafts especially once they get wet& you'll be fine. I bred & hand fed/raised a variety of birds including cockatiels, Indian Ringnecks, & lovebirds. I dabbled into American singer canaries & Gouldian finches.
You could always use wild branches especially off fruit trees so long you know they are not sprayed. Manzanita branches are a good choice too. Extremely hard (to hold to little beaks), with plenty of branching pieces would be a good choice too. Google it there's lots if suppliers, some with bolts already drilled into them for easier mounting options. I always liked it because it was easy to clean if/when it got soiled. Little soap & water does the trick just fine.
Glad to see your enjoying them so much. They are fascinating animals.