There are three main ways of getting across the gap.
Option one ($900) is a boat from Cartagena in Colombia which takes approx. 15 days and you can pick the bike up in the port in Panama with all of the correct paperwork this does require some research and to pre-book which wasn't right for us as we on looked one day in advance, so we took option 3.
Option 2 if to fly the motorbike from Bogata which in hindsight is the best option as you can fly at a similar time and is the safest way, however, there is only specific flight which you can use.
we heard about people who used DHL which cost $1000 ish and the need to pay on top and addition for themselves to fly to Panama.
Option 3 (winging it) ($600/700) if you look at the map above you can drive to Turbo and start the journey. This is definitely the most dangerous way as you are given a captain of a speedboat your life, and worldly possessions on a highly pirated sea with your hundreds of dollars in cash. We were fine however it could have gone wrong as a recommendation other tours are going on to try and find a fellow traveller who could recommend a captain for you. Be prepared to get bread and spam for four days and deal with a lot of chop.