After all about the importance of a good source (player, instrument, good DI/amp) was said already - did anyone mention fader riding?
Riding the bass is essential - as with all other main elements that should be prominently heard but not overwhelming the mix... Some of the pop references mentioned have huge kick drums - and in the arrangement there's no bass on those spots or mixed very low - and when it should come out and add drive - there you go - fader up... How many times I noticed that the perception of punch and even the subjective audibility of bass line in the arrangement improved when I put the bass lower in the mix on certain spots (and I love it up front otherwise).
You should do several passes of fader riding and painstakingly put it in the picture - once with a very loud playback and once listening very softly, to hear how it purrs and drives at the low level. To everyone - don't be lazy with low cut, compression, side-chain compression, etc. to separate the elements - do what the name says - MIX - and it looks like the word says - up and down, up and down and around.
Editing (and/or good playing) is the key, too - the accents should fall tight as hell - cut the separate notes if needed and put them where they kick ass not muddy the picture. When nothing else helps I EQ separate cut splices if some notes jump out too much or don't jump out as they should - but that is rare. Riding the level is usually enough. That way you don't need to compress for even sound, but just for the desired effect and can compress less if it is not needed for the sound and get a more lively bass - and you take care of the "eveness" with fader riding...
Parallel compression can be very helpful, too - I used to overdo it, but now I almost forgot about it in my everyday "routine" - but it can really make space and punch at the same time... I guess I get good enough (for me) bass tones without that recently.
Among the compressors - I mostly use 1176 and CL1B (UAD and softube plug-ins) and they work as they should. I also got very nice compression on bass with Neve Portico 5043 - both HW and Steinberg plug-in. It is a great clean, but smooth compressor for bass - to make it sit nicely in the mix - my subjective feeling about that compressor is - that it is a POP compressor, whatever that means to anyone else.
Not for the pop references - but for the really excessively fat and round bass tone - Daniel Lanois gave out one of his approaches - cranking the amp and boost the low end and playing with a very soft touch - but that is more for huge soft purring bass...