Playing only the roots of the chords in quarter notes is a perfectly fine way to accompany a soloist or play with an ensemble. However, it can quickly become overly repetitive and lack expression. One of the first things to do once you can track the roots through a tune is to start adding the 5th of each chord to your bass lines to start getting movement and variation.
Be sure to count the 4-beat groups aloud while practicing, this will prevent you from losing count 1 otherwise known as the “downbeat”.
“...Some instrumentalists like for you to be like a rocking chair for them… [plays R-5-R-5 etc…]” - Milt Hinton
If you have a combo, or a group to play with, try these bass techniques with a drummer and chord player to hear how the quarter note locks with the ride and hi hat cymbals. Chordal players will probably play syncopated rhythms that work off the quarter notes of the bass and drums.
Focus on getting a good sound on your bass, keeping steady time, and locking with the drummer. If you play electric, take measures to emulate the sound of an upright bass by palm-muting or playing with your thumb. In all cases, aim to keep your quarter notes full value, almost bleeding into each other.
Practice creating your own bass lines according to these principals. Any 12-bar blues will be a good starting point, but you can also apply these techniques to jazz standards and anything else you want to swing. To learn faster, write down your bass lines (in whatever method works for you) and practice them in order to get the concepts “under your fingers” through repetition.