Just wear cargo shorts. I wear them with either an IWB or OWB holster all the time with a t-shirt.
Don't carry off of your body, if you get thrown off of your bike, you no longer have your gun.
Not sure of a brand name but there are compression shirts (like under armor) that you can buy that have a holster built into the shirt around the ribs. Or you could look into a belly wrap holster. Just google belly holster or shirt holster.
What is a "third shirt"?