A starter circuit is pretty simple.
Starters draw a lot of current. You would never run all that power through a push button. Rather, the starter button just activated the coil in the starter relay. The relay handles the high current. Generally speaking, the distance between battery and relay, and relay and starter are kept fairly short.
When you look at the relay, there should be a small gauge wire coming from that. Many relays have two. In those cases, one will be wired to the hot side of the ignition, and the other will go to the starter button. The starter button grounds that wire, completing the circuit and activating the relay. Others with one wire requires that power be supplied to that lead to activate. Those require two wires to the handlebar start button... one hot wire, and the wire leading back to the solenoid.
I think that your bike may have a two-wire starter relay.