Your idea of going to some open mic nights and singing with a guitar or mandolin is sound, as this will build up your confidence. However, as @ubit mentions above, singing and playing bass at the same time is often a very different ball game, due to syncopation. I used to sing lead vocals on China Girl and the second half of that was a nightmare, but repeated practising at home finally nailed it (sorry, it’s the same old ‘keep doing it’ advice, but it’s true). Another potential pitfall is not committing to the performance. I found that if I was tentative at all with my vocal delivery, my pitch would suffer, but this is just a confidence thing that improves with more and more performances, both at home and live.