If you are going to attach the tripod to the bike somehow, make sure that the bungees or whatever do not impair the movement of any cables or levers. The tripod is likely to shift a little over bumps and stuff, so make sure that it's not near any moving parts - pedals, spokes, chains, wheels, etc... Poorly secured, and the moving tripod can cause some serious harm.
And if it's 22" long and you try to put it in a backpack, there's a chance that it may interfere with your helmet, or worse, be anywhere close to your neck or head in even a minor spill.
The safest way is probably on a rear rack. The standard racks have two mounting points at the seat cluster - where the seat meets the bicycle frame - and one on either side of the bike by the axle of the rear wheel. The struts that go from the lower mounting points to the rack itself helps to keep stuff away from the spokes of the rear wheel. Here's an example:
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There is a newer kind of rack that mounts in just one place - to the tube that the seat is connected to. From there the rack cantilevers back and floats over the rear wheel. This kind is much easier to use and can quickly be moved from one bike to the next. This would be a nice platform to bungie a tripod too.
Hope this helps.