Can I get a Bluetooth Subwoofer?

The answer to this, as many things in life is, Yes, and No. Yes technically you could get a Bluetooth subwoofer but it would pretty much only give you bass and everything else would sound terrible. Also, I've never seen one. If you find one put it in the comments.

But I see bluetooth speakers on Amazon that say subwoofer. 

Yep, you can find speakers on Amazon and elsewhere that say Bluetooth and subwoofer in the same product description. They are almost always referring to the fact that the speaker has a passive or active subwoofer built into the speaker itself. Another way is to have a 2.1 bluetooth speaker system whose subwoofer is attached to the main speaker(s) via a wire. This enables the sub to get a signal.

Why can't I get a standalone Bluetooth Subwoofer?

In it's current form the Bluetooth spec does not support sending signals to two separate devices. It can send a stereo signal which one device can receive and then split to separate units, usually via a wire. The unit would send the mid-range and high signal to one unit in a stereo pair and that speaker would be responsible for using a cross-over to send the signal to the subwoofer and the other side to the other speaker.   

But I want a separate subwoofer!!

There are solutions wireless speaker solutions hat offer separate subs like Sonos, but they do not employ Bluetooth. Sonos uses a proprietary Mesh Network (think WiFi) to send signals to different speakers. Sonos systems sound great but they are expensive. 

What to do?

The folks working on the Bluetooth spec (warning link will hurt your head) are updating things all the time. It could be that this is in the works as I write. In the mean time the best solution for getting better bass through an out of the way subwoofer would be either something like a Sonos system or a small two-way system. 

Another choice maybe coming this week. Google is rumored to be announcing a Chromecast Music for this week. We'll see how that plays out.

Also check out the top consumer rated bluetooth speakers on Amazon as of September 2015