I'm pleased to read that many bassists here get the concept of 'warming up' much better than (say) in a guitarists' forum

where they would go all mad suggesting an hour or more of technical exercises and call it a warmup...
Personally I believe the warmup is only about two things: getting your body ready, and getting your mind ready, before you start your serious music activity (be it either studying/practicing, rehearsing with your band, or playing a show).
Getting your body ready includes getting physically comfortable, washing your hands and removing distractions (drink or eat a snack if you're close to thirsty/hungry, have a quick trip to the loo...). I wouldn't normally call these 'warming up' but they're part of a good starting routine anyway. In the winter, there are days when I also literally need to warm my hands from the freezing cold if I've been outdoor, so I might keep them on a radiator or under hot water for a couple of minutes.
Sometimes I do some stretching or rotational movements to loosen up the joints (hint: Julia Hofer from Thomann has a good video on those!) before even picking up the instrument. Not always, this depends a bit on how I feel, there are times when I really need this and others where my joints feel fine and I can just go straight to the bass or whatever.
Then, the key thing for me is to first do something on the instrument that doesn't require focus. Usually, I just play randomly on the neck using all fingers, gradually increasing speed and adding various techniques, for a few minutes until I feel ready. During these minutes, I can feel that my hands get going, and most importantly my mind gets 'into the zone', at the beginning of the warm up I'm always on a sort of autopilot and nothing sounds musical, but gradually I can see my mind waking up and wanting to seek some grooves and melodies, and becoming attentive. Then I know I am ready for a focused practice, rehearsal or performance.
I do not time my warmup by the way, that would be quite a dumb thing to do IMO, I am ready when I am ready.