Recommendations for headphones under $400?

Sennheiser Momentum's do a nice job, AKG and HiFiman

Lots of good options at $400 or below, actually. One of my go-to pairs for rock and pop at work is the PSB M4U 1 (which I pair with a dragonfly red). As far as performance for the price it is an excellent choice. Great options at the high end of this price range and with ample bass are the Master & Dynamics MH40 and the OPPO PM-3.

Yes I know there are LOTS of options at this pricepoint, that is part of the problem...lol.
I really do not know a great deal about headphones, by that I mean the names and models that are the best.
Sennheiser I remember having numerous pairs back in the 70,s and 80,s and thinking were excellent value for money at the time.

Sennheiser is still excellent value for the money but IMHO you're not really getting an excellent product until you're up into the 650 range or above. And since your primary criterion was good bass response for rock music, I'm assuming you want to stay away from open backed designs (which the most beloved Sennheisers, including the 650 and especially the 800 are). 

I'd absolutely think about (and preferably try to listen first) to the PSB, M&D, and Oppo options. All are in your price range and offer strong performance.

Not sure how big of a basshead you are, but, for the money, I'm pretty happy with AQ Nighthawk.  Enough bass for most of my listening.  Some folks don't like them, but I find them very comfortable and non-fatiguing.  Easy to listen to for long periods.  They won't rattle your brain very much.  Pretty sure they can still be bought new for 299 with generous return policies.  25 ohm, so can be a problem with some amps.

A lot of folks are raving about the Focal Elears and being 90% of the Utopias.  Pop up occasionally for around 550-600.  If it's 90% of the Utopias at that price, probably can't go wrong.  Bass on the Utopias is quick and solid, but not yuuge,  Love them.

I'm a headphone noob, within the past year, other than always having something cheap around just because.