You could just do something like a kitchen trash pull out that a trash can or hamper fits into. This might be better so that if wet or particularly dirty clothes get put in the bin it's easier to keep clean.

My hall bath has a pullout hamper. It was in the cabinet when we purchased the house so I don't know if it came with the cabinet but I do know that the cabinets are not custom. We seldom use our hall bath and there is no need to use the pullout as a hamper. You are right though it really wouldn't hold but a few clothing items or towels. It does however work great for toilet paper storage.

Our hall bath came with a pull out laundry hamper. I use it for storing Kleenex boxes from the Costco run. It's too small to hold much laundry and ours is wood so anything damp would mildew quickly.

Look for some custom cabinet shops in your area and ask for an estimate. If you know what you want they can give you an estimate and you get to decide. We have custom cabs in our bathroom that I love, and custom-sized cabs from a larger mfg in our kitchen. Turns out that if we had gone local to get the kitchen cabs it would have cost less. No harm in making a few phone calls.

-Babka

We had one like badgergal's in the master bath in our old house and we definitely used it. for dirty clothes (not towels, I agree, that would have filled it up too fast). The kids' bath had their own (used less frequently - they used their bedroom floors as hampers LOL)

Oh, sorry, those cabinets were not custom - they were Crystal.

Ours takes the place of the middle and bottom drawers in a drawer stack. It's kind of like a pullout for trash, but is a wire bin similar to above. We have one in our MBa now and like it enough to include two in the new house. You are right it doesn't hold a ton if you start putting jeans and towel in it, but it will hold a lot of the small stuff that seems to end up there (socks, underwear, tshirts, washcloths.)

Our first one came with a canvas liner with handles, and the idea that you'd haul it to the laundry. I rarely do that, I just transfer to a basket when ready to do a load. I just didn't want a laundry basket on the floor in my closet collecting stuff, so this has worked well. I don't sort until I get to the washer though-- heck, who am I kidding, I barely sort anyway...

I don't want to put totally wet washcloths in there though, so I dry them out a bit on the tub deck first. I could just see getting a moldy mess in there. The new ones are just the metal wire structure, no canvas liner. I could make one later if I think I need it, but I doubt it. Our cabinets are custom, but I think he just got the baskets from RevAShelf.

Our double custom vanity was not cheap, and I would change somethings

(fake drawer above pullout), but I wanted a laundry pullout and am very happy with it. We looked online for a laundry insert, but ran out of time, so they built this instead. Ours did not come with a canvas liner, but I found one at TJMaxx that I love. Sometimes we pull out the whole thing and sometimes we just dig the clothes out. We accidentally ordered kitchen depth, so we are able to get both darks and light. Previous vanity's laundry was one tilt-out chrome wire basket that I also liked, but the jumbled clothes, especially delicates would catch on the wire. BTW trash basket is by toilet.

Our lst house had one similar to Badgergal that worked great for me. You could remove the wire basket and take it to the laundry room. It held plenty and I think the Kraftmaid cab was about 60 inches long, one sink in the middle, drawers on the right and the hamper behind the door on the left. There was a working drawer above the hamper.

Now I have 2 laundry baskets in my new ( to me) house that rest on shelves in the master Bedroom closet. I think this closet is bigger than my last one. About the same as far as usefulness.