I am a bass player (started on piano, then played guitar since I was about 10, then played bass fiddle). I am female and do not have unusually large hands (but I have pretty strong fingers from playing bass over the years). Because you have some choices of which string you wish to play to derive a certain note, with practice you can figure out how to play a tune without a great deal of left hand stretch (at least on a fretted bass guitar). And because of the design of the instrument, the thicker strings can be played with your stronger fingers and your weaker fingers (pinky) is in perfect position for the higher pitched, less thick strings. To build up finger strength, I often squeezed a small ball in my finger tips (a tennis ball was too big for my hand size).
Maybe due to the order I learned the different instruments, how I think of playing them are very different. I don’t think I rely much on my mental sense of the piano scales when I am playing bass but I think in terms of circular patterns when I play both guitar and bass and piano feels more linear to me somehow.
I don’t think you will have any trouble learning how to play bass guitar. I suggest finding a few songs you like (not your band, but recorded music with a decent bass part) and playing it over and over with the bass turned up and the treble turned down. Start with your instrument in its case and just listen to the bass parts. Get to where you can hum the part and feel like you know all the bass notes of the chorus (for example). Now take your guitar out and figure out the notes. This can be a slow process, but if you learn the part before you try to find the notes, it will go MUCH faster.
There are a number of songs with excellent bass parts that are interesting to learn. Once you get a sense of what bass players are doing by learning a variety of covers, then you can start to figure out bass lines for your band’s original material. You will be pretty limited in what you can write without getting a real sense of what other players do first.
You didn’t indicate what kind of music your band plays, but if you would share that, we can probably name some good bass players for you to listen to and learn from in the style you are interested in learning.