There are a few mobile friendly bass centric headphones I would recommend. Note: I’m not an IEM guy, so I’ll let others cover that if they interest you.
Fostex TH-600 (and the numerous Foster variants like Emu Teak, Denon D5200, TH-X00, etc). The stock earpads can feel a little cramped, and I personally use the ZMF Suede Universe pads on my Emu Teak. Those pads even out the sound without killing the fun. These can be put into a travel case for easy transport
Meze 99 classic. These are just fun and easy to drive. They look good too. Meant to be portable.
One I personally am not too keen for, but others seem to enjoy are the Mr. Speakers Aeon 2 Open or Closed. These definitely need some kind of amplification. Also, one is a bass cannon and the other not so much. You can read about them here
You could pair all of those with an Asgard 3 or Jotunheim 2 w/ internal AKM dac card for a very respectable desktop setup. The JDS Element II is also good.
For on-the-go direct from your phone use, check out something like the iFi Hip DAC or AQ Dragonfly Cobalt.
For “on the road” use, please don’t use these while driving.