Regardless of whether you have taken antibiotics, so long as you are a carrier of the MRSA bacteria, you are potentially contagious. So in effect, you stop being contagious when the bacteria is no longer in your system.
How contagious is MRSA?
MRSA, or Meticillin Resistant Staphylococcus Aureus is a "super bug" which causes so much damage due to it's resistant properties which make many antibiotics so ineffective at treating it.
MRSA is particularly contagious among hospital patients as they often have an entry point for the bacteria to enter the body (usually in the form of a surgical or open wound).
Treatment by a non-resistant antibiotic should clear up the infection, but will not effect the amount of time that you are contagious for. If you are a carrier of MRSA, you are always capable of passing it on to someone else, although if you have an active infection with symptoms eg. Boils, abscesses etc. you are more likely to spread it, as the infected area will contain lots of MRSA germs. This is why it is important to get antibiotics into your system as quickly as possible, and why you should always finish your course.