I'm not sure that the fact you are a bass singer makes a difference to the question of trying to sing higher - I think that singing higher could be a goal of both basses or tenors, and so I offer some general advice for singing higher.
First off, do you understand what your falsetto is? Every male singer has a falsetto, and while you may never be able to sing some of the high tenor sweet tones in some popular songs, it is still worth seeing if you can extend your falsetto. There are other questions on this site (and surely resources elsewhere) that can help you to extend your falsetto.
While I don't have much experience teaching singing, I think it might be good to consider placement also. It isn't proper singing to always sing from the chest, so if you are doing that, try moving the sound into your head - or toward the front of your mouth and not down in your throat. Hooting like an owl is one way to see the difference immediately. The sound of your voice will be brighter the farther forward in your mouth it is, and you will certainly extend your range by using your head!
As the other answer by Snoooot mentions, it would be good to just work it higher by singing higher. You don't even have to find music necessarily - why not pretend you are a monk and sing your own gregorian chant, and slowly get a little higher each time?
If you are serious about singing, try joining a choir or find an outlet for your voice. You will get much better advice in person.