There are certainly quite a few options for you, but I'm nervous that the pressure sensor you're using is only meant to measure the kind of pressure differences you'd get from changes in (air) altitude- not (water) depth. According to this spec sheet, the BMP085 only measures up to 1100 hPa which translates to just slightly over one atmosphere of pressure.
That being said, assuming the sensor can handle being in a liquid as long as the liquid is not conductive, I'd recommend placing the sensor in a zip-lock bag, rubber glove, or other flexible container filled with mineral oil. The oil won't short out any of the electronics, but will equalize to the pressure of the water around it. Surgical gloves (such as latex or nitrile gloves) also are a great source for the sort of membrane material you're describing. Keep in mind that the sensor you have seems to have a hole in it which allows air to enter the chamber where the sensor is, so a membrane may not be able to push directly against the sensor as you describe. If you were planning to keep the sensor inside a container filled with air, and you were hoping the movement of the membrane from water pressure would pressurize the air to reflect depth, you should also remember that air is compressible, so there may be a hard-to-calculate relationship between the pressure you see and the depth you're at.
Anyway, you seem to be working on a cool project, and I hope it works out. Please let us know how it works out, and don't hesitate to ask of you have any other questions or ideas to bounce off of us!