Are you asking about a wooden clothes basket that you carry or a wooden hamper? Don't think I've ever seen a wooden clothes basket and wouldn't it be heavy?

Wooden clothes hamper but actually bamboo or a light wood like that is fine.

Can you post a link to what you are looking for? Not quite sure what a laundry basket would be used for in a bedroom. Is this just to carry items upstairs from the laundry?

I'm sorry I meant laundry hamper.

I have a 3 hamper hanging system that is great. Its on wheels, hampers are fabric on hanging hangers and can lift off to move. Someone else on the forum has the same one. I got mine at Costco 5 or so years ago. I wash the hampers rarely. I keep it in my basement. I wouldn't want any bamboo or wood, cause I'd be afraid of snagging my clothes. I believe this is the same one at Amazon for cheaper:

https://www.amazon.com/dp/B00MIOR5Y0?tag=amz-mkt-fox-us-20&ascsubtag=1ba00-01000-org00-mac00-dsk00-nomod-us000-pcomp-feature-pcomp-wm-2-wm-1-wm-1-wl-ask1&ref=bit_pcomp_ask

Otherwise I've been to the container store and have picked up several carrying baskets that I adore. One is made in Germany, soft sided plastic with handles, and the other a very nice larger plastic hamper with fold down handles made in Japan. It has a very upscale look for plastic, LOL.

The German tots, are great for taking laundry upstairs. I have 2 and got them at the Container Store:

This Japanese made hamper from the Container Store, is in my "posh" bathroom/laundry setup, sitting inside an open cabinet shelving: