I have had 4 turb's for non invasive bladder cancer and have decided not to have BCG treatments. Can I just have my bladder removed?

Not standard. Local bladder therapy such as BCG and others can put off the need for bladder removal for quite a period. Bladder removal can be done but urine pathway reconstruction will need to be surgically done too. Your urologist can discuss other local treatment drugs besides bcg. Finally, many centers are looking at robotic bladder surgery.
Sometimes necessary. Depends on grade (aggressive nature) of tumor. For those with low grade disease, turb often is curative. However, for high grade disease and recurrent disease resection alone is not enough, and we recommend bcg. For someone with recurrent high grade disease, some urologist may advocate for early cystectomy (bladder removal) but many will advocate a course of bcg. Was yours low or high grade?
Be careful what you. Ask for, you might get it.. Cystectomy or prostocytectomy, with urinary diversion is something to adapt to when you need it. Deciding not to have BCG and opting for cyctectomy sounds petulant. Discuss this with a few urologists, experienced with both, and air your reasons for spurning the relatively benign BCG for the more than you know cyctectomy.