True!! Honestly, as someone who plays all three instruments - piano, bass, and drums - I can say that all three are all of equal importance when it comes to the overall groove (which is essential). Obviously with piano being my primary instrument, I know a bit more.
With the piano, accenting some parts of each measure helps it swing even more. Specifically, since swing is built from triplets, accenting parts of those helps tremendously. During the bass solo, playing on downbeats to help keep the time.
On drums, you hold the stick so that it's loose in your hand, so that it can flop easily. (This is different from classical drumming where (at least how I was taught) you hold the sticks with your index finger on top.) This makes it so you don't have to move your wrist as much when you play swing time on the ride cymbal. Hitting snare accents on the triplets (sort of the same thing as on piano) is essential, too. Obviously keeping time (beats 2 and 4 usually) on the hi-hat is the most important thing.
On bass - and this is something that a lot of people struggle with (that I did, too when I first started playing) - you need to play legato - that is, notes connected, not separate. This is a challenge for beginner bassists, because doing this while moving around the fretboard is very hard. Just takes a lot of practice! In fact, I was just teaching someone how to do this yesterday! Playing legato (and being so much on the quarter note that you're almost a little bit early) is what makes the whole band swing. This is why I say the bass is the most important instrument in a jazz group. Also, adding in some pulls/ghosted notes here and there is good.
