The most basic approach to bass would indeed be to play the root notes of the chords and follow the rhythm. Choosing which string to play on would need to take a few things into consideration. You can just play the note wherever you find it and that will give you the correct note but the other aspects to consider have to do with tone and texture.
A lot of times you want to play the bass note an octave below the guitar's root, as this will broaden your frequency range, adding more depth to your harmony and providing a strong feeling of support, which is largely the function of basic bass parts. The bass is tuned an octave lower than guitar, so if you know your root note of your guitar part, you can just play it in the same place on the bass, ie, same string and fret.
Next, we want to consider tone. As you may have noticed with guitar, each string has a slightly different tone about it, which is most noticeable when playing the same note (same pitch/same octave) on different strings. You should find that the same note played on a lower string will have a thicker/rounder tone to it. This has a lot to do with the thickness of the lower pitched strings having more low frequency strength but also has to do with the length of the vibrating string. Anyhow, in some approaches to bass, whether it's style or genre, it will make a little more sense to play a note that could be on the A string on the E string instead, to add this thicker tone to the mix, but in other situations, you may want a thinner tone that has more high end clarity.
Where you pluck the string can also affect the tone quite a bit. Plucking closer to the bridge will have a thinner tone than plucking above the pickups and plucking near the neck will have a more round tone with less high end clarity than plucking above the pickups. I would recommend experimenting a little with this by playing a single note and changing up where you pluck the string, or recording the bass line once for each spot (near bridge, over pickups, near neck). This should put you in touch with how it affects the tone and can allow you to make an informed decision about which will best suit your music. You can of course pluck the strings in between those spots as well, such as midway between the neck and the pickups but I suggest starting at those three points first to get in touch with the concept and better able to hear its effect.
Similarly, if there is a pickup selector on the bass, which is a good bit less common than on guitars, your tone should be affected similarly, where the bridge pickup will be more thin and your neck pickup will be more round.
Beyond all this, you can then consider whether or not you actually want the bass note to be an octave lower or not. The bass having thicker strings will inevitably have a thicker tone than guitar while playing the same note in the same octave. Sometimes it can be nice to play the same pitch and just add the thickness to the tone instead of adding the depth of being an octave lower.
A lot of times when I am choosing which octave to play my bass notes in, I also consider the overall range that I will need to cover. I'll also consider what key I'm in and what note I want to be the lowest. So if I'm in G, I might want the G to be the lowest note I play, as it would have the thickest sound and encourage a sense of resolution. In such a case, if the chord progression has an E minor in the mix, I may choose to play those Es above the G instead of the open E, probably on the A string, so that I can maintain G as my lowest note.
In short, you can usually just choose to play the bass note an octave below where you play the root on the guitar, which should work fine but to add a touch of nuance, you may want to consider the tone and octave placement. I know you mentioned that you don't want to full on learn to play bass but I would suggest taking a close look at it and trying to get in touch with how it affects your music. It could change how you approach writing on guitar when you know there will be a bass player involved in the music.