Agree with you. I have a lowepro slingshot 3, very nice bag, and my tripod case has backpack style straps. I can wear both, and do, but I wouldn't even think of getting on a bicycle with it. It is very cumbersome and awkward, not to mention uncomfortable, but at least this way I can shoot while I'm hiking.
Is there some way you can lash the tripod to the diagonal down tube on your bicycle? Not talking about a pvc tube, just a carry bag like this one:
B189 Adorama Tripod Case Medium (25")
I think it could work, they also have a bit longer bag for a few dollars more. As long as it doesn't interfere with either peddaling or steering it might work.
NaCl(just a thought)H2O