Alder - This is considered to be the most balanced and versatile of any bass tonewood. That’s why you will often find it on basses that are focused more on versatility than one set sound. If you want one bass for any style check out Alder.
Ash - Ash is very similar to Alder tonally but it does have some slight differences. With Ash you will generally get a bit more high end and faster attack. These small differences make this the perfect wood if you are a slap player that also needs to play with a pick or fingers as well.
Mahogany - Mahogany is a deep warm wood that works brilliantly for picked and fingered styles that need to really hold up the low end in a mix. The main issue with mahogany is that is weighs a lot which when used on such a large instrument can make it a pain to play.
Basswood - Warmer than Alder but not as dark as Mahogany, Basswood has an interesting sound that you will either love or hate. It has a beautifully balanced sound but with a bit more low end to carry the mix. This is most commonly used on basses with active preamps as it lets you take advantage of that balanced sound.