They could but Bellator barely spends any money on advertising, (for whatever reason) it's just not their style.
If he was cheaper he would be a great opponent for Kimbo or Lashley, but I don't know if he's worth the money in North America. The hardcore fans know he's not a serious fighter, and the casuals don't know him at all. He makes great money in KSW and is very valuable to them, so he wouldn't come cheap, if they could get him. Remember KSW said they don't lend out their top-fighters, and (even though he's not) I bet KSW considers him to be one of their top-fighters in the same way that Rizin considers Akebono to be a star.
I could see Bellator going after Fallon Fox though, especially since she has a netflix documentary now.