You are most right to consider the bounce factor.
I used a 2x6 pressure treated board & strapped a the rear wheel to the 2x6. (through the spokes)
NOTE: the 2x6 went all the way under the front tire too. I screwed in about a foot of 1x2s on both sides of the front tire to keep the front tire from sliding off the 2x6.
Later I found a 1x6 channel of AL & that became my KEEP in place track for the VStrom & anyother bike that kept resting on the tail gate.
Plywood will work but does not remove the down ward shock while going over rough roads as well as something stronger directly under the bike's tires.
Have seen some very creative designs from guys who had not tail gates at all & still in short bed trucks.
One guy used his ramp to support the rear tire over hang.