If the speakers are indeed from the Acoustimass product line and not the Lifestyle product line, then yes, you can hook them up to a regular receiver.
Can you specify how many individual components there are? (i.e. two speakers that are connected/twistable would be ONE component). I'm not sure if you are implying that you have a left/center/right/surround L/surround R or just left/right.
The "Bass Module" (it is NOT a subwoofer - subwoofers play low frequencies, a "Bass Module" plays lower mid-range frequencies) should include a special cable that is a pinned connection at one end (the end that connects to a special port on the bass module) and bare speaker wire pairs on the other end. These speaker wire pairs get connected to the receiver's speaker terminals.
As Sam indicated above, any modern AVR will work in this situation - they will all have analog stereo inputs to connect an iPod or other portable music device.
In addition, if you are adding a receiver to the mix in order to utilize the Bose speakers, then the TV speakers are no longer needed and should not be used. You should change the way your cable/satellite is connected. The receiver should be the "hub" of your system, NOT the TV. So, you should connect your cable/sat box (and Blu-ray player, game system, any source really) directly to the receiver via an HDMI cable, then run a second HDMI cable from the receiver's output to an input on the TV. With this setup, you will be able to enjoy true 5.1 audio for all sources connected to the receiver.
If you connect all your sources to the TV first, then run audio out from the TV to the receiver, then any 5.1 from your external sources gets lost and downmixed to stereo.