Could deep vein thrombosis in the leg be caused by a bicycle gash on the leg?

Not very likely. If the gash was associated with tissue trauma like a crush injury with profound bruising and immobility, then a DVT could be possible, as dr. Press said. But if you only had a cut without much oterh deeper tissue damage, it is unlikely.
Possible, not likely. Dvt are usually associated with immobility, so if you were immobile after any kind of injury, the risk of DVT would increase. However, i don't think the injury you describe would, in itself, increase the likelihood of this happening.
Possible. If it is a very deep gash that has disrupted blood flow it could contribute to a DVT but it is probably not related.