You'll need both a midi pickup and a controller. The
Axon is the best on the market at the moment, because it detects notes with the pick transient, which (provided you are using a pick) is a lot quicker than the Roland units. It also has a software editor and a lot more options when it comes to zones, splits and layers of midi data.
There's always going to be some latency with midi bass (especially when using the lower strings) but you can simply play an octave higher on the bass, and then set your synth an octave lower to solve this. All of the midi pickups are basically the same design, and will work with any guitar to midi controller. There's also custom piezos that you can install into the bridge which are even better than the external pickups.