My 2G 600 used to shake the bars at approx 70kph. I felt it was a combination of a number of things:
1. Front tire wear and config - I was using BT56 & BT20 tires which have two centre grooves and block patterns running to the side. These tires seemed to cup or scallop easily.
2. Front tire on my 600 was a 120 - 60 series, or low profile. The 1200 Bandits have a 120 - 70 series.
3. I have the front forks dropped 5/8" and rear preload on full to tighten up the turning.
I changed the tires to a set of Michelin Pilot Roads, with a 120 - 70 series front. With this change in tire size and pattern, I now have NO hint of wobble. The larger profile makes the steering a little heavier, like the 1200 Bandit, so more stable for highway trips, which is where I normally use the bike. If I were spending my time in a city setting, I would use the lower profile front and live with the shake at 70kph.
For your bike, check the front tire for signs of cupping wear and make sure it has enough pressure. Low air pressure and scalloped wear seem to aggrevate the problem, IMHO.