I do not remember the trill drills in Simandl 1, and can't reference it as my copy was "borrowed" several years ago and has yet to be returned. If you want to work on trills, my suggestion is to work on controlling the speed of your trills. Instead of the relatively common spasm-between-two-notes method, if you listen to recordings of soloists (not necessarily just bassists, but Joel Quarrington's trill at the end of the Bottesini Elegy is fantastic) you will find that trills can vary considerably in speed, and often speeding up or slowing down during part of a trill particularly on long trills adds a lot musically.
As an exercise, I would practice that by putting on the metronome and slowly moving between the two notes. Keep your left hand relatively quiet and close to the fingerboard as pulling the finger you aren't using way off out into space is a bad habit in general, but especially with trills, and make sure both notes are even sounding and both engaging and releasing your finger is a clean motion. Then speed it up. Start with quarter notes and then move to eighth notes, eighth note triplets, sixteenth notes, sixteenth note triplets etc. until you are playing quite quickly, and then slow it down again. Listen to what you are doing and see if you can hear both notes clearly, if the top or bottom note is more pronounced than the other, etc. This can also be a bow issue instead of a left hand issue, as we have a tendency to neglect the bow when we are working on something challenging with the left hand. Also don't think of it as lifting your finger and putting that same finger back down again with it being a motion isolated to just your hand, but more like turning a doorknob and rotating your hand/arm with your thumb as the pivot point. Trills are very similar to vibrato in that regard.
If you are using Simandl technique, then you will want to be comfortable with trilling between 1-4, 1-2, 2-4, and T-1, 2-3 in thumb position, so you can trill in any position for a tone or a semitone. 2-4 is going to be the hard one, but you should be able to do it so you don't have to use an even more awkward fingering to accommodate a trill you are incapable of. There will be situations where you will making fingering adjustments to make a trill more comfortable or to allow you to be more expressive, but if it is a quick trill in the middle of a passage, that option might not be as readily available to you.
Trills and vibrato are very closely related, so it would be beneficial to work on them both.