There will hundreds of opportunities for you to save some money on your trip to Bangkok, whether you avail them or not depends totally on you.
Bargain with tuk-tuk drivers
Rikshaws in Thailand do not run on meters, so you will have to do a classic bargaining with the driver. Most of the drivers are usually expecting some bargaining, so they originally quote a high price so they can bring it down to a considerable one when you object. So, don’t simply say “ok” to whatever the driver says. Also, ask from the locals to get an idea of the cost of the trip, and don’t climb in until a price is agreed upon.
Insist that the taxi runs on the meter
Many of the taxi drivers will prefer that they give you a ride on a flat rate (which will be higher than the original cost) instead of turning on the meter. Insist that they turn on the meter for the ride, if they don’t listen, move on to the next one.
Public transport is the cheapest
Public transport in Bangkok is really very cheap and quite convenient. If you can handle a crowded bus or train, it would save a lot of your money if you used the public transport.