As a rep for our local association, I attend the ABC national convention every year. There is always a rules seminar that discusses rules interpretations and equipment specifications that may not be directly covered in the rules book.
The issue of two handed bowling and/or fingerless/thumbless bowling has been discussed in detail. Neither is illegal. However there are restrictions. In order for a ball to comply with the static weight requirements (max top/side/finger/thumb weights) a ball needs to have a grip center. For most balls it is defined by where the finger and thumb holes have been drilled. In an undrilled ball, the bowler defines the area by where the ball is placed in his bowling hand (ie label in center of grip etc.) When bowling two handed, the position of the dominant or release hand determines the center of the grip. The release hand is generally the right hand when delivering the ball from the right side of the body. That delivery needs to executed from the same side of the body for the entire competition.
Confused yet, there's more!!! In a drilled ball, the bowler may palm the ball but needs to position in his hand so that the finger cover or are in the direction of the finger holes and the base of the palm is oriented over the thumb hole. If the holes are drilled for gripping purposes, they define the center of the grip and the static weights are measured from that location. It is legal to deliver a ball without using the grips, however the ball needs to be oriented the same way in the hand for each delivery.
By the way, the maximum number of "holes" in a bowling ball is 12. One for each finger(5), a vent hole for each finger hole(5 more), a balance hole, and a mill of inspection hole normally used to test coverstock hardness in PBA events.
Hope some of this helps.
