As has been said, it's illegal to cohabit with a member of the opposite sex if you are not married.

As has also been said, it happens - so long as you both keep quiet about your real relationship, most people will assume you're married anyways. You must be aware that it only takes one vindictive person to make a complaint about your living arrangements to be arrested and deported (hopefully with no jail time). In 8 years in the Gulf, I've only seen this happen once - but you don't want to be #2 here.

If your accomodation is in the same building/compound as your business colleagues - it will be difficult to keep your secret. You cannot sponsor your GF so getting a tourist visa renewed on a regular basis will run you about QAR1200 per flight to Dubai (not sure about Bahrain prices).

Again, as someone else mentioned, better for her to apply for work and get her own sponsor.

Cost of living - malt & hops beverages can run QAR45 at a 5* hotel to QAR24 at a less swanky location. Same for meals out - sky is the limit at the big hotels, a burger and fries elsewhere maybe QAR40.

Groceries - Australian/NZ steak (say rib eye) about QAR40/kilo up to QAR75 or more for Tbones. Brocolli QAR30, loaf of bread QAR8 for something better than the fluffy white stuff (whole grain with seeds etc.) Any specialty items from Europe or North America usually carry premium prices but sometimes you get lucky. A box of wheat thins crackers runs QAR35 here and QAR10 or less in North America.

Cars - you can do a quick search on here to give you an idea of what used cars are going for.

Hope this helps