Nope. MBD isn't caused by bacteria, it's a calcium deficiency (caused usually by low calcium in the diet or too much/little vitamin D, which impedes calcium absorption into the bones) but wouldn't be affected by antibiotics unless there was a secondary infection.
The best way to halt the deficiency and correct blood-calcium levels, in short, is to analyze why the chameleon has MBD in the first place (did you use a good, new UVB bulb? Did the chameleon get supplemented with plain calcium frequently? Did the calcium have vitamin D3 mixed in as well?) and then correct. Usually a vet is a great idea in this case, as they can do a blood test to see where levels are, give a liquid calcium injection to get the chameleon started, and monitor the treatment.