Following from Neale's reply.

The BoB is basically a collection of discrete inputs and outputs. One, by design, is able to drive an onboard relay. One other is able to drive a PWM output. But, apart from these functions, they are all just bog standard discrete outputs.

Now, the problem you have is interfacing to the VFD. The inputs to the VFD need to be pulled low (connected to ground) to activate. You *could* connect these directly to the BoB outputs (any of, including the relay output... more in a second), but the problem is they are likely pulled to 12-24V internally to the VFD. You don't really want to connect the outputs from the BoB to something at that voltage (though, it's likely to survive through the internal clamp diodes on the logic outputs). But I digress.

OP - you show that you basically understand an NPN transistor switching element. Use NPN transistors to provide the switch-to ground (collect -> input, emitter -> ground), and a 4k7 resistor (or near-neighbour) to any of the unclaimed outputs on the BoB, Two - one for forward, one for reverse.

With that configuration, remove the jumper for the relay (unnecessary) from the BoB. Then, an active-high signal into the BoB from Mach3 on the corresponding pin will activate the corresponding input into the VFD. As Neale suggests - you can re-appropiate the B-axis outputs - whichever pins they are bound to - just use those to create outputs within Mach that you then bind to the forward/reverse "relay" pins in the Mach3 configuration page.

I'm not able to look at Mach3 to give precise details at this time, but speak up if that's less than clear.