As you imply, we generally don't want to lead into a chord change with the root of the new chord.
Options:
1-1-5-2;
1-8-5-2 or 8-1-5-2;
1-5-2-5;
1-3-5-2;
1-3-2-5;
8-6-5-2;
1-6-5-2.
Plenty of Blue Grass and CW basslines feature
|1-5|5-2|
This is root 5th for I and V chords.
Obviously if the progression is I V I V I V... for an extended time, you don't want to play the same pattern all the time. But I don't think you have to particularly avoid ever playing |1-5|5-2| ...just don't play it all the time.
I would also suggest adding some walk ups and walk downs.
You might play |1-5| then jump down the octave to
5 in bar two to camouflage that you are repeating the same note; then walk back up to the I |
5-67|.
|:|1-5-|
5-67|1-1-|
5-52|
|1-16|5-2-|1-1-|
5-65|:|
Note: Depending on the arrangement and the musicians you are playing with, the preceding 8 bars may be considered great or way too busy. You might only want to do a walk up/down at the end of the 8 bar phrase, and stay squarely in two the rest of the time.
Hopefully my notation is clear. A number followed by - is a half note, for example 1- indicates a tonic half note. Tow numbers together are quarter notes, for example 67 indicates a quarter note played on the 6th and 7th scale degrees. Bold and underlined numbers are played below the tonic For example
5-67 is a half note played on the 5th followed by quarter notes played on 6th and 7th walking up to the tonic.