The ANT BMS or the LTT/JBD Smart BMS do have bluetooth. The LTT/JBD apps are originally for e-bikes/scooters/carts, so it has a distance left option in the app (the default), or just a charge left option. I’n not sure how the ANT does.
As for the amps required you will have to look at the specs for the motor. A smaller BMS will still work, but will have a lower top speed.
This is the BMS that both @TheTerribleTriplet and I have. You can check his thread about it for more details. It is a very nice BMS and I have written a driver to connect it to a Victron system (there is also a thread for that) so it talks to it similar to an expensive battery like the Pylontech. It is also sold in the USA as a Overkill Solar BMS.
There are many models. Choose the one that fits your needs best.
Just make sure it is a smart model and that the app looks like the one in my post (it should - but then you are guaranteed it will work). They all come with the bluetooth module that is connected to a UART (RS232). The easiest is to get one that also support a RS485 port (easiest is also to get the PC USB cable from them). Then you can connect the bluetooth and to the driver/PC at the same time.
Are you going to use it with Victron, @JohanB bought a Battery from Baine, and it was literally plug and play with Victron. I am not sure what you want to do, but the smart BMS in his new batteries seems to be work quite nice.