There isn’t a single “bps” placeholder, but you can build it with the movement deltas. player_position_delta_x/y/z give you blocks per tick, so you can calculate horizontal speed in blocks per second with a calc placeholder.
Example:
{"placeholder":"calc","values":{
"decimal":"true",
"expression":"sqrt(pow({"placeholder":"player_position_delta_x"},2)+pow({"placeholder":"player_position_delta_z"},2))*20"
}}
That gives you the horizontal BPS (multiply by 20 because there are 20 ticks per second). If you want full 3D speed, add the y delta into the sqrt as well.
You can find those delta placeholders on the Placeholders documentation page.