I made one out of walnut, but it gets pretty ratty after one washing.

Don't have any idea whether this will work, but if the dishwasher is
producing a raised-grain effect, you might try sanding down the spoon,
washing it again, and sanding it again. As I understand grain raising,
it should get less ratty every time until it pretty much stays the
same. If I'm off base on this, I'm sure someone will correct me. It
sure wouldn't hurt to try, though.
I do know that bamboo tends to stay nice and smooth even after several
cookings and washings, but of course it's not available at most local
lumberyards...
Try some experiments, have fun with it, and let us know what works,
Andy