If you have a genetic potentional for large forearms then your going to get them much larger whatever you do, benching or not. True the forearms help to stabilize the upper arms and shoulder girdle throught out the benching movement but as far as being responsible for any noticeable growth, I would doubt that very much. If PL'ers or the one lift wonders who only do benches, have huge forearm it's not from benching. I've seen some very strong lightweight's push up some massive amount of weight in the BP who's forearms looked like sticks (no insult intended for these guy's). I've also seem some of these same guy's DL outstanding weight with those stick forearms. Not always how you look but what you can do.
As Onlyme mention about the thumbless grip and bar mostly resting on the heel of the hand, most of all the heavy bencher's I've seen all use that style rather than thumb over and crading the bar in the palms of the hand. Get a more direct line of force (power) with the heel in a straight line with the wrist, more or less. With the thumb over, your over flexing and putting too much pressure/stress on the wrist it's self and lossing strength in the push. The only way the forearm comes into play is with the stablization of the bar during the lift.
Working on the grip alone will not always build size in the forearms but will increase strength. If you want better size than try BB wrist curls with the bar resting on the knee's while sitting. Curl the bar from the tips of the fingers all the way up to a tight ball with your fingers only. You can do this reverse style (thumbs facing down) but this affects the grip more. Stand with two DB'd at your sides and just curl up the weights with your fingers. Take a full sheet of newspaper (I suggest the LA Times, not much good for anything else) and grab it at one end and just keep wadding it up into a tight ball. Doesn't sound like much but it should kill the forearm muscles. Hang from a chinning bar at the tips of you fingers and try curling just your hand into a tight ball, another killer. Try BB reverse curls or Zotterman DB curls, very effctive for better forearms. A wrist rollar (12" dowl with a light rope attached and a BB plate on the end of it) is also a good movement. Dozens of other forearm exercise out there. Good Luck.
