No
The seal on a ziploc bag is not sufficient to keep water out. When you put it underwater, even less than a couple of metres, the water pressure will press on the seal & cause it to leak.
The flexible housings made by EWA-Marine that fhotoace mentions have proper seals that are watertight to several metres.
Other alternatives are to buy a camera that is waterproof to a rated depth (most of the consumer 'underwater' compacts are suitable for swimming pool use), or
buy a rigid housing for a camera (if one is available for your model).
If you're in the UK, Cameras Underwater are a good supplier of quality cameras/housings;
http://uk.answers.yahoo.com/question/answer?qid=20100604000934AAFFORc
and here's a selection of mostly consumer models from Amazon;
http://www.amazon.co.uk/s/?ie=UTF8&keywords=underwater+camera+digital&tag=yahhyd-21&index=aps&hvadid=37082190531&ref=pd_sl_9cyppyr5ve_e
I dunno where Forlorn Hope got the idea that a bag would burst - due to water pressure, it will get squashed, not burst. In fact that's the problem with flexible bags - as well as leaks, the water pressure tends to push buttons you don't want pushed!