Nick,
I can't tell you the specific height, but I can tell you an easy way to find out. Purchase, or go to a vendor's store and measure, the stock wood blocks that act as the spacer between the front bed cross sill and the frame. By memory they are approximately square and about the same width as the top of the frame rail in that area.
Steve


1950 Chevy 3100
261, 4 speed
Purchased 1977

1964 Pontiac Lemans Convert