Audiobus v3 has been launched and this may be all you need.
The app already supports Garageband (along with hundreds of others) and they provide an SDK (software development kit) for other app developers. This too has been updated to support new functionality included in version 3.
What I do know
I know of someone who owns the Behringer UCA202 (not the Behringer UFO202) and has used that to route incoming audio from a guitar via a genuine Apple Lightning to USB Camera Adapter to an iPad 4 and then outputting that audio via GarageBand using the Audiobus app.
While it's not the same Behringer unit as you have, my understanding is that the only real difference is that the Behringer UFO202 you have foregoes the digital stereo out to provide a switchable PHONO input for old turntables such as yours.
Also, I remember them having issues at first until they used a genuine Apple Lightning to USB Camera Adapter. They couldn't get it to work with a cheaper 3rd party adapter.
What I don't know
Whether this person has ever used this process to route the audio from the iPad to an external Bluetooth speaker. This is something I will try to determine.
The only other thing I'm not 100% certain of is whether they used anything else to get this to work, but from memory it was just a combination of the Behringer UCA202, a genuine Apple Lightning to USB Camera Adapter, the Audiobus app and GarageBand.
If that's the case, then you should find that what you want to do is possible with Audiobus and GarageBand.
Okay, this is what I've since learnt after originally posting this answer.
As I mentioned previously, I know of someone who owns a Behringer UCA202. Now, it seems they did try for a little while to route music to a Bluetooth speaker, but with mixed (mainly not good) results. They tried doing this via Audiobus directly and in conjunction with other apps.
This prompted direct contact with Audiobus support and below is a quote from the support email they got back:
Sorry, Audiobus does not play well with Bluetooth speakers. I cannot
recommend using Audiobus for this use case. Bluetooth audio is always
terrible for live audio, because it adds latency. That’s why we’re not
supporting it. Any wired speaker will do - they don’t have any issues.
As routing music wasn't their main use case (they were mainly interested in recording guitars), they didn't pursue it. However, if I was in your shoes, it may be worth trying Audiobus in conjunction with a 3.5mm to Bluetooth transmitter. I'd wait for Audiobus 3 to be released first, and then I'd look at transmitters such as this. (Note: This is just one I picked at random - I have no affiliation with the seller or product).
My thinking is that Audiobus will see something like this as a wired speaker and that this could result in you achieving what you want.
Obviously, only you can decide whether the costs of buying the app and transmitter are worth the expense, especially since it's purely to experiment with and with no guarantee of success.
Hopefully someone else will come up with a confirmed solution, but if not this may be it. All the best with it.