In survival mode, I am completely unable to use a bucket on an axolotl that is on land or in flowing water. I continue to hold an empty bucket on pressing "use", and get no bucket 'o axolotl.
I have difficulty with capturing an axolotl in a bucket when one is in water source blocks as well (hitbox may need some tweaking), but can do it successfully.
I think this works as intended, does the bucket you're holding contain water? You can only pick up mobs in if the bucket already contains water.