I guess you have an unfinished basement.

Depending on how much space you have, you could use one of the high efficiency polystyrene boards - I'm a huge fan of ISOboard, it's got a very high R-value per inch. I'm not sure if it's rated for direct contact with hvac ducting - heat makes plastics brittle over time (which is why we put a pad of insulation between electrical wires and hvac and dryer ducts.

If it's tighter, convention would be to use ordinary wall-type insulation, and tuck it between floor and duct. Better yet would be to use Rockwool which is used between floors for soundproofing and fire-rating. It's much more dense.

As an additional layer, you could use the mylar foil-bubble wrap stuff immediately under the floor (again, I don't think it's rated for duct contact, I don't know. It's reflective, so combined with one of the others it might help.

I've heard bamboo flooring can be a problem with low humidity, have you checked your humidity levels?

I'd also talk to the manufacturers of the flooring and check what they say about installation. If your ducting is correctly installed and not leaking (you should wrap the joints with the appropriate foil (not 'duct tape') then the flooring should not do that.