I used to ride. I didnít ride very well and considering discretion being the better part of valor sold the bike.
I think a shoulder holster would be a good choice. Printing can be an issue during the summer months of lighter covering garment due to bending forward on the bike. A shoulder holster wonít do that.
I have heard people say they carry left handed on a bike. Considering most cars canít match a bike for acceleration and maneuverability, I think I would stick to right handed carry and drive out of a situation if I could. If you arenít mobile and canít escape, you will have full use of the right hand to draw and fire.
"Patriotism is supporting your country all the time, and your government when it deserves it." -Mark Twain