Here is some other good reading about "transitioning". In short, most people will agree that it isn't transitioning, but learning an entirely new instrument.
You will obviously retain your knowledge of the role a bass plays in an ensemble, your musicianship, etc. but there aren't a whole lot of similarities after that. Unlike switching between acoustic, electric, or classical guitars and to a lesser extent bass guitar, you are really stepping into fundamentally different territory. It can be done and there are obviously a lot of people who double, but it is going to take a lot of work.
We all strongly recommend seeking out a qualified teacher. It is very easy to develop poor technique that can lead to serious injury.
Although very few double bassists like to talk openly about it, (as it can lead to losing work) most have faced injury at some point in their careers. Some have had to stop playing entirely, some were able to come back after rest and therapy, and even more play in various amounts of chronic bass related/induced pain.
None of the above is intended to scare you (too much anyway) but to encourage you to pursue this "the right way". If you do so and you really want to learn, you can and will be successful.