You can use the Spark as an audio interface. Guitar to Spark, Spark USB to computer. The USB output mutes the amp speaker, so you'll need decent computer speakers. There's probably a setting on the Spark that's as clean as possible, which is probably what you want if using the Spark as an audio interface to then feed your signal into Bias.
I can't tell if Bias is a VST. If it's a VST, you need a DAW to host it - Ableton, Cubase, Reason, Logic, Garageband, etc. If not, I guess just rock and roll in Bias.
Take the Spark out of the picture, and you'll need an audio interface. I use a Behringer 4-channel with great success - low noise, low latency, pretty solid.
If you haven't messed much with guitar --> computer, be wary of latency. Read up on your sample size, buffer rate, etc. It can be tricky to get instant response like you do with an amp... and doing so is a whole 'nuther set of questions and investigations.
Also be wary of getting too attached to the guitar --> computer setup. It's hard to take anywhere, software needs updating, drivers can break. It's just fussier than guitar --> amp.