I use a regular 6 racquet bag with teh backpack straps, no problems at all.
Safety tips. Assume EVERYONE is an idiot and cannot see you. I ride two large red motorcycles with the lights on ( no, not at the same time, be quiet!) and I may as well be invisible half the time. Just act like every vehicle you see is about to pull out in front of you and you might survive..
and, unless you want other bikers to laugh at you, forget 'special attachments' for carrying ANYTHING!
5.0 all courter. 2 x Dunlop Bio 400T with cyclone @ 50, 1 x Dunlop Bio 400T gut @ 55
"Tennis isn't easy" - Corners