I think you have read these instructions on the MSDS already however to reiterate here is the skin contact info and what to do. Note the last point in bold.
Skin Contact:
In case of contact, immediately flush skin with plenty of water. Cover the irritated skin with an emollient. Remove
contaminated clothing and shoes. Wash clothing before reuse. Thoroughly clean shoes before reuse.
and importantly!!
Get
medical attention.
Even if that is just a triage to check her skin for any reactions or burning etc.
When anyone has an accident in the lab if you are at all unsure what to do the first thing is to contact your institution's safety department. They are not there to get you into trouble. They are your first line of defense in an emergency (no matter how small). If you are working out of hours they will always have someone on call. They will have people there trained in how to deal with the worker if hurt and/or the spill if serious. They will be able to reassure you as to what to do ....and that may well be to do nothing!
I would not EVER advise pouring bleach on your skin. DON'T RESPOND TO A CHEMICAL SPILL WITH ANOTHER CHEMICAL! You never know what the consequences might be, especially if you are already panicked. Just flush yourself with water and lots and lots and lots of it. Get under an emergency shower if it's big. That is what they are there for. Your modesty is always secondary to your safety in these circumstances.
Now this is overkill in your case, but worth remembering for a big accident, that if necessary, your safety department can also coordinate the emergency response so as not to confuse fire/police/EMT that may need to arrive from off site who do not know where to find you if you are on a large campus like most universities.
So in short, talk to someone in the Safety department. It will put your mind at ease if nothing else.
As for the shirt, if it is really that valuable to you, wash it several times by itself like the MSDS says and then re use. If it is really that valuable why wear it in the lab? Lab coats tend to catch the worst of spills if being worn. They're dorky but functional. You'd have no qualms about throwing out the lab coat and getting another if that caught the spill.