MD recommended bandages and ace wrap applied in!clinic remain on for 24hr, then move to compression hose, can I switch earlier?

It will be fine to wear medical compression stocking 20-30 mmHg after sclerotherapy. Keep compression stocking for a period of 1 week, only during the day time. Try to avoid lifting more than 20 pounds for two weeks, avoid strenuous exercise for a week, and avoid sun exposure for 4 weeks. 
Best, 

You can do that if you like. It is important to wear stockings for at least 2 weeks and for up to 3 months after sclerotherapy.You need to use some adjunctive measures after sclerotherapy to reduce post inflammatory hyperpigmentation. it is those that don't follow such instructions immediately following sclerotherapy, starting on day1 (next day) that seem to get retained hyperpigmentation. I recommend 2 creams: Scleroquin plus and Sclerovase and also Scler-X supplement to reduce post inflammatory hyperpigmentation (see link below) as well as compression stockings for at least 2 weeks.
H Karamanoukian MD FCS
certified vein specialist from ABVLM and double board certified surgeon

I give my patients a choice of ace wraps or compression hose post sclerotherapy.  You can certainly remove the ace wraps and wear compression hose immediately.  There is no benefit to waiting 24 hours to change the ace wraps.  The important thing is to have post procedure compression.

Yes it is absolutely fine to take off the bandages and wear your compression stockings anytime after sclerotherapy.  I recommend wearing them for at least one week.  If your bandages are falling off, then you are correct that they are offering you no compression at this point.