A CR2450 has quite a large capacity for a coin cell, but is not capable of providing enough continuous current for this application.
Here is a typical CR2450 datasheet
It says for continuous dischage, it is rated at less than 1mA, which is nowhere near what your BT module requires.
Even for a brief pulse, the rating is only 9mA for 2 seconds. This graph from the datasheet is quite informative:
You can see the IR (internal resistance) starts out at ~15 ohms and rises quite quickly. Given this info you can calculate the voltage drop at different currents. For instance if you want just 10mA, then you will get a voltage drop of 0.010 * 15 = 150mV. At 100mA this is 1.5V!
Steven mentions a capacitor and short bursts of RF. This is certainly possible (one of our products uses a coin cell and does a similar thing) but may not be suitable for you application.
So, you will have to select a different battery. Nowadays you can get very small Li-Ion batteries that would be good for this application. Have a look on Mouser, Farnell or maybe eBay - I recently bought one of these for a prototype:
For 500mAh (not sure if this is accurate, haven't tested it yet. I expect it to be between 300-450mAh) it's very small. The dimensions are given as:
EDIT - what about an AAA with step-up?
This would work okay. It would drain quite quickly though as the battery would be providing more current due to the step-up and efficiency. For example if we have a 1.2V nominal NiHH AAA, and your BT module requires 3.3V at around 50mA:
50mA * 3.3V = 165mW.
If we assume an 80% efficient boost converter then:
(1 / 0.8) * (0.165W / 1.2V) = ~171mA required from the battery.
A typical AAA is about 850mAh, so you can run your module continuously for around 850 / 171 = 5 hours.