Easy enough, you need to look at the circuit board. Typical USB Powered speakers can be broken down into three parts. Part 1 is the USB Sound Card. This is powered by 5V and accepts a USB connection and decodes the audio. Part 2 is the amp stage. As most USB soundcards have internal pre-amps, there will only be one or two identical 5V amplifiers. Most amps can power two speakers in single ended mode, or one speaker in dual/double ended mode. Finally, Part 3 is the speakers themselves.
To know what wattage the speakers are designed for, get the part number of amplifier IC(s) and look for the datasheet. That will tell you the maximum wattage. And then sketch out the circuit. 9 out of 10 times, the circuit on your speakers will match the Typical Application/Recommended Design/Layout Schematic in the Amplifier datasheet. The actual resistor/capacitor values and layout will tell you the actual wattage it is designed for.
Again, 9 out of 10 times, the circuit will match the typical application for both the usb sound card IC and the amplifier ic, be a simple single or double layer board, and be fairly easy to figure out. Shouldn't take more than an hour, even for a beginner.
To add in your bluetooth control, replace the USB sound card IC with your bluetooth audio driver. Leave the amplifier in place unless you need to change it for some pointless reason :D.
Update: The posted circuit board only has one IC, the TP6902 (or clone). It is an old (2005) all-in-one USB Audio Controller, USB HID Buttons (Maybe), and two D-Class amplifiers built in. Each channel can support up to 5v * 346mA or 1.75W. The typical being 200mA or 1W. So those speakers are probably not more than 2.5W each, and the only way to mod the speakers for bluetooth is... completely replace the IC with a custom Bluetooth Audio receiver + D-Class Amplifier board + LiPo Battery + LiPo power regulator. The only thing that you would be using is the case and the speakers themselves.