Is the output amplified? Turntables put out phono level (as distinct from line level) audio. In the olden days, the amp accounted for this by amplifying the phono level differently to your standard AUX (line level).
I only ask because I would guess your stock Bluetooth transmitter wants the higher 'line level' input and wouldn't play nice with phono level.
I know some people like the ceremony and experience of the turntable and the LP's, but if you just want sound, why not hook it up to the computer and record all the records (hehe) to MP3 so you can play them back without the hassle. You probably have all the cables you need making it free too!
Or you could go all out and upgrade to a bluetooth turntable