HC-06 Arduino Nano Embedded Project?

I don't know if the software serial will work if it's slow. Maybe I should be more specific.
The project is not a single LED, it's a 16x16 LED Matrix:

https://drive.google.com/file/d/14whhAoXe4I85A--owvhVrnugu9NhdASK/view?usp=sharing

I want to make a snake game that can be controlled via the smartphone Bluetooth app.
It needs to be fast enough for somewhat fluid game-play.

Another idea I had was to make a switch that would disable the TX / RX lines of the HC-06.