Edit: I've added a list of all the existed known comapnies
Stock Market With BTC List:
1broker.com (played up to 1 btc smooth deposit/withdraw - 25.5.16)
simplefx.com (unknown - need reviews/proofs)
bitbulls.com (SCAM - check their name on google for proof)
everything about your terminology is wrong!
- you don't bet on the stock market (unless you are fool rich kid with money to waste)
- you don't play with 1 btc,...
- instead you bust your ass learning how to trade, and then learn technical analysis and then some stuff about economy and related stuff and after than you start researching and busting your ass finding a good stock to buy and then invest and hope for the best.
if you want to gamble, go do it in a dice site!
I want to point out that technically while i have not found one place that offers what the op asked you can bet sort of on the markets. There are sites not necessarily in bitcoin but ethereum and so forth. They let you bet for example will the nasdaq close up or down on a certain day or how many percentage points.