Having been in a couple of motorcycle crashes, I'm convinced the second safest place is in front of you, to one side or the other of "Capt. Happy And His Two Crew". Basically in front of your pelvic bone.
There are no really fragile organs there - there's the femoral artery and some colon/intestine but both are very tough compared to the kidney, spleen and liver. The pelvic bone is ridiculously tough and even if it breaks, it tends to heal up OK. You also tend to "fold forward" around your waist.
This means either front-crossdraw open-carry, or a fanny pack. The latter carried this way is a great choice for bikers in my opinion.
If you're going to do a shoulder holster, left side is better because it's not over your liver, one of the delicate organs...
The ABSOLUTE safest rig puts the gun in a pack that drops down from the belt and straps to your thigh, on TOP of the main thigh bone. That is one hell of a tough bone. I slammed mine into a steel stop sign post at 25mph while flying sideways one time, hurt like you would NOT believe the next day (literally couldn't walk) but the bone held. If that won't break it, I have no idea what will
I'm considering modifying my fanny pack for that sort of carry. It's somewhat oddball, but...it can be made to work and gun access is decent both sitting and standing.