For how long will a venous ulcer using compression bandages take to heal?

Venous disease. A great and common question that is asked. We cannot tell without additional information and seeing how each patient responds to our treatments and modalities. There are so many intervening factors (other diseases, infection, acceptance of recommendations, etc.)
Treat cause first. Venous stasis ulcers are due to venous hypertension which is usually due to refluxing (malfunctioning) valves of usually the saphenous or perforator systems. If you are simply wearing compression bandages then you are not addressing the cause of the problem and the ulcer may heal over a long time only to recur. You should see a vein specialist for a venous reflux exam to find the ulcer cause.