You can indeed have a bladder infection without the common signs of pain, or itching, or burning or other discomfort.
If you are not peeing sufficiently, the urine can back up and cause a kidney infection -- NOT a good thing.
I don't remember -- have you been diagnosed with MS? It's possible that you have what is called a "neurogenic bladder" -- the muscles (and the bladder is a muscle) aren't opening and closing properly, are "out of sync", so you'll feel the urge to pee and not be able to...or not feel the urge, and suddenly you've wet yourself.
Yes -- see a urologist. You can be tested for all of this, and if it is a neurogenic bladder, there are meds you can take to help with it!