Driving a Chinese spindle VFD from mach3

[JAZZCNC]

So I'd run a wire from my BOB to a relay then to one of the terminals on the VFD and I'm guessing I have to connect the grounds of the VFD to the BOB?

No on the VFD there's Signal terminals for Run/stop and direction. You take a wire from the DCM terminal on VFD and pass it thru the contact of the Relay on the BOB then back to the Run terminal on VFD.
Then when the G-code fires M3 command the output on the BOB turns it's on board relay on and the contacts close making the Run signal active. When the G-code fires M5 the output goes OFF and relay closes it's contacts.

EDIT: If your BOB doesn't have Relay then you can use a separate Relay and control thru the output of the BOB but the relay coil must be able to work with the low current that will probably come from BOB output.

You can do the same for Direction but don't recommend you do that has you'll rarely if ever have need and it's easy to miss type 4 (M4) instead of 3 and spindle start in reverse.!!!!

For speed control you have to have some way of Digitally controlling VFD IE: RS485 or using Analogue signals and sending the VFD 0-10v signal to it's analogue terminals which control speed.
Problem with Analogue is you have to have some way to convert Digital signals coming from the PC back to analogue and at the correct voltage 0-10v. Zero being Off Ten being full speed and all voltages in between being relative to the speeds setup in control software.

To be honest I rarely use Speed control thru G-code and just control thru VFD but do have G-code start and stop spindle then i can walk away knowing it will stop when done or if E-stop occurs when I'm not around.