National Bumper Pool Association

“No player is allowed to jump his ball over balls or bumpers in making shots. Penalty for this will be same as in Rule Seven.”

“If a player sinks one of his opponent's balls there is no penalty, but if he sinks one of his own balls into his opponent's cup, or shoots one of his opponent's balls, his opponent may then drop two of his own balls into his cup.”

“Rule 3.24 says it is illegal to "dig under" the ball to get it to jump . . .”

“3.26 ILLEGAL JUMPING OF BALL
It is a foul if a player strikes the cue ball below center (“digs under” or “lofts” the cue ball) and intentionally causes it to rise off the bed of the table in an effort to clear an obstructing ball. Such jumping action may occasionally occur accidentally, and such “jumps” are not to be considered fouls on their face; they may still be ruled foul strokes, if for example, the ferrule or cue shaft makes contact with the cue ball in the course of the shot.
3.27 JUMP SHOTS
Unless otherwise stated in rules for a specific game it is legal to cause the cue ball to rise off the bed of the table by elevating the cue stick on the shot, and forcing the cue ball to rebound from the bed of the table. Any miscue when executing a jump shot is a foul.”

“JUMP SHOT: A shot in which the cue ball or object ball is caused to rise (jump) off the bed of the table. (If this is caused by a player elevating the butt and striking down on the ball, generally the shot is legal. If, however, the player digs under the ball, causing it to jump, the shot is a foul.)”