If your technique is correct small hands won't be an issue when playing bass and having small hands doesn't require a thin neck or short scale bass. Esperanza Spalding can play an upright bass with no effort. Checkout how she plays upright and electric basses.
How you hold the bass and how high you play the bass makes reaching the strings easier or harder. If you can't reach the lowest string without stretching or feeling uncomfortable hold the neck at a higher angle until you can. Some people play with a sharp angle to their wrists. I find it's more comfortable and easier to play if the wrists are straighter.
Whether you use 1,2,3,4 (1 finger per fret) fingering or 1,2,4 depends on where you are on the neck and what the next note is. Generally use 1,2,3,4 higher up the neck, above the 10th fret, for instance, but I'd always, always use 1,2,4 fingering below. Don't stretch (ever), so don't fix your thumb to any spot on the back of the neck. Always move your left hand to place your fingers over the correct fret. Aim to move your left hand for every fret change.
Watch videos of Rocco Prestia and Travis Carlton. They'll play whole lines with one finger, just moving their hands to the correct place. Move your hand a lot and your fingers a little.
If your left hand is moving properly then you'll be hitting all the notes without stretching. Always focus on your fingers and the note and in the end your hand will follow.