Most bluetooth standards available will introduce latency. The key usage is for pressing "play" and expecting to hear music sometime later. Not that your pressing "play" (or any buttons) and what comes out the other end have to be perfectly in sync with near zero latency. TV sets that use this technology have a picture that travels at the speed of light - and bluetooth is much, much slower. In that case, the TV has a way of delaying the display in order to compensate. When you're playing the keyboard - there's no way to delay your fingers to compensate.

The way to get rid of latency with bluetooth speakers is not to use bluetooth. Most have an auxiliary input for direct-connect. They tend to be 3.5mm stereo connections - so a cable terminated with the correct ends is necessary. I have a "bag" full of adapters that includes a 3.5mm splitter to take 3.5mm stereo male plugs and present 2x mono typically RCA connections on the other side. Then I have 2xRCA ("stereo" ) male-to-male that I plug into there and the other end each RCA male connector plugs into a female RCA to TS 1/4". The RCA cable is fairly lousy unshielded stuff - but does the job. There are other adapters that can be used to limit the amount of "lousy cable". Or it may not matter considering the general fidelity of bluetooth speakers in the first place.

Note there are some standards of bluetooth where latency is reduced. These standards do not tend to be implemented in most bluetooth speakers, headphones, or transmitters due to lack of need for the intended application.