I use a mix of white vinegar and olive oil to clean my kitchen table and it gets off stuff I didn't even know was there! I've seen different ratio's but I've found that 3 parts vinegar to one part oil works best for me. The vinegar cleans and the oil conditions the wood.

the stickiness most likely is caused by partially oxidized oils from the dressing you have used.
A cleaner like 409 and a plastic scrubber will remove it....but don't do that if the bowl is varnished.
In that case try just dish soap and lots and lots of elbow grease.
Linda C

Hot water, dish soap and elbow grease, but don't let it soak in water-the wood will warp. Good luck!