Not to sound simplistic, but it depends. There are several consumer protection statutes that protect consumers, but if bought "As Is" then you may be out of luck. Professor Richard Aldeman at UH Law School has some great information online to help consumers. I also recommend you contact an attorney to discuss your options. Find an attorney with experience in breah of warranty, breach of contract, and DTPA experience who won't charge for initial consultation.
If you bought the bike "as is" then you might be out of luck. If the seller made representations that were false, them you might have grounds to sue for breach of warranty or DTPA. You wold need to seek out a lawyer experienced in those type claims. This question was posted in the personal injury section. You might repost is a section that contains lawyers who deal with consumer issues like this. Best of luck.
As the other lawyers mentioned, you may have a breach of warranty or some type of DTPA claim (Deceptive Trade Practices Act). This depends on a number of factors the most important being whether you purchased the bike "as is." I would advise you to contact a lawyer that may be able to assist you with pursuing a claim against the seller. If you do not wish to obtain legal representation, the best thing for you to do would be to file in small claims court. Your easiest route is to seek the cost of repairs from the seller. It would likely be difficult to rescind the entire transaction and obtain a refund for the bike, but this does depend on the facts of your specific situation. First, get an estimate for what it would cost to repair the bike. Once you have the repair estimate, you could file suit in small claims court against the seller. There is limited discovery and you don't have to worry about the rules of evidence in small claims. The judge will basically listen to your side, then listen to the other side and rule accordingly. It will cost you about $131 to file, but you'll receive that back as long as the judge rules in your favor. If the seller represented that the bike was in good condition and it was not, then you will likely succeed. Best of luck.