Welcome to the Forum!!
From your description, it appears that this is the most common form of bladder cancer, sometimes referred to as transitional cell or urothelial cell carcinoma. The papillary form is like a small mushroom that extends out into the bladder cavity. Low-grade means that the cells are only slowly dividing, while high-grade means that they are dividing more rapidly and have a higher chance of spreading if not treated. There is a lot of information if you go to our Home Page underBladder Cancer 101.
This form of bladder cancer is highly treatable when found early, as it seems this was. Often a urologist will do a second TURB (the biopsy surgery) to make sure that he/she got all the possible tumor and to be sure of the diagnosis. The urologist may also recommend a form of immunotherapy called BCG which is often highly effective, particularly in the case of high-grade bladder cancer.
As I mentioned above, this type of bladder cancer can be very effectively treated. For example, I was diagnosed with a similar type 14 years ago, received BCG treatments, and have been cancer-free every since!
Sara Anne