Your problem is that will result in a poor quality, non hi-fi sound. The quality bottleneck is the Bluetooth link and the amplifier at the speaker end. If you're using the old amp, then presumably you're using speaker level signals. To get that to the Bluetooth speaker, it needs to be digitised, transmitted to the speaker AND then reconverted via a DAC and amplified to speaker level again. Most Bluetooth speakers are cheap affairs that have a basic DAC and amp build in. But seriously, what quality do you think you're going to get unless you're spending multiple hundreds of Euros. And if you're gonna do that, there are better ways to go.
You could try looking at a new amp with a digital output and a moderately expensive Bluetooth speaker? But why would you? Wired is the way to go if you want quality. If you're happy with lo-fi, just stream from your phone. It'll be just as good as the turntable/amp combo via Bluetooth.
This is 100 % accurate, Bluetooth is not a patch, on a fully wired analogue system. I do use it regularly for convienience only, but it pales in comparison, to my all analogue wired vinyl->amp->wired speakers.
Allthough, i have heard good reports on hi res streaming, IF, you have the right gear, Amazon HD, QO Buzz etc, coupled with a decent DAC, but not alas Spotify, which stubbornly continues to be low res, however, blutooth is undoubtedly a very handy solution, when on the move, in your car, away on holidays, or a kitchen setup.
But what i have found in recent years, is that Spotify is where i hear music first, or check in on a new band thats playing or whatever, so i am learning a lot about new material or previously unheard material, playing vinyl, is mostly music i already know, but the sound, if you have good gear, betters, well, everything.