I'm thinking the bar ticks up about 1 exp per 1 game minute tick... bar-wise anyway. I guess it's technically half that since only half that bar is actually extra exp. Either way, my original thought was it was 1 exp per second but after a night in the inn I found I had about half what I expected so 1 exp per game minute tick on the clock seems more accurate. I can't say I've noticed a cap but I know I've gotten a full bar as a 40 cul which was 70k+ tnl. I'd guess if there is a cap it's probably 50k bonus or 100k bonus, but I would half hope it wasn't that low.