I looked up the WPA rules and they clearly give players a lot of latitude for use of the bridge. I've highlighted two sentences, and please note the word "or" in the first sentence; it is NOT the word "and", which would have been considerably more limiting. To me in reading this, I do not see how an official could say it was illegal to use the that cross table bridge, with your bridge hand supported on the bridge shaft. You are "supporting the cue", you are using it "for the purpose" that it was intended, and you are doing the "configuration ...up to the player". If the WPA wants that to be illegal, they need to re-write their rule. It definitely says nothing about the bridge head needing to be in contact with the table. I know sometimes I find I need a bridge at the rail, and I have to balance the bridgehead on the rail/cushion, not rest it on the table.
1.3 Player’s Use of Equipment
The equipment must meet existing WPA equipment specifications. In general, players are not
permitted to introduce novel equipment into the game. The following uses, among others, are
considered normal. If the player is uncertain about a particular use of equipment, he should
discuss it with the tournament management prior to the start of play. The equipment must be
used only for the purpose or in the manner that the equipment was intended. (See
6.17
(a) Cue Stick – The player is permitted to switch between cue sticks during the match, such as
break, jump and normal cues. He may use either a built-in extender or an add-on extender to
increase the length of the stick.
(b) Chalk – The player may apply chalk to his tip to prevent miscues, and may use his own
chalk, provided its color is compatible with the cloth.
(c) Mechanical Bridges – The player may use up to two mechanical bridges to support the cue
stick during the shot. The configuration of the bridges is up to the player. He may use his own
bridge if it is similar to standard bridges.
(d) Gloves – The player may use gloves to improve the grip and/or bridge hand function.
(e) Powder – A player is allowed to use powder in a reasonable amount as determined by the
referee.