They can be found in Ventureland, Lonesome Manor and Tomorrow City. The ones in Ventureland as mentioned above are mechanized pirates (they also reappear in the Train Tunnels. In Lonesome Manor, they are the Skeletons (who also appear in Epic Mickey) probably based off the short cartoon, the Skeleton Dance. In Tomorrow City, the Bashers are dressed as Maximilian from The Black Hole.
To defeat a Basher, you'll need to use Thinner to erase their armor. However, Paint is useless against Bashers, as all machines have no emotions at all. Once the armor is gone, he will try to attack you by spinning, where he will stop and show his weak point (which is a green button), use the Spin Move to do some damage to him. Like all other Beetleworx, Paint will slow him down.
In the second game, a new variety appears, based on Tik-Tok from Return to Oz and in the credits an unused chef basher appears (most likely based on the one from the Autopia ride). The unused chef Basher also appears on a sign in Autotopia.