I don't think a barn door is the best bet for keeping noise from the master bath out of the bedroom. I do think you could put in a premade regular door with a little bit of work. This is actually a great homeowner project. You'll do a little bit of framing, then some drywall, then hang the door, and add some trim.
Since your opening is 36x90, it would be easiest to actually make your opening smaller so you could fit a standard, off the shelf, 32x80 prehung interior door. The rough opening will be 34x82 1/2".
First you'd make a little ladder out of 2x4 lumber with 2 pieces 36" long, and three pieces 4 1/2" long so that the while thing is 36"x7 1/2". Nail or screw that to the top and sides of the opening. Make sure it's centered, so the drywall can be patched in on both sides. Then on the hinge side of the opening, nail or screw a 82 1/2" piece of 2x4 with a strip of 1/2" OSB behind it. Again, make sure it's centered so you can add drywall.
Add some drywall, blend it in with painter and paint, then hang the door and put up some door trim. You'll probably have to remove the baseboard on the inside of the opening, and have to cut it back a bit so that the trim lines up right.