Strong Bass Headphones Under $200

Feels like I might be over recommending this to new members of head-fi... but for me personally, the mdr-v6 from sony has clean, crisp bass. Might take a few hours (burn-in/adjusting to sound sig) to get used to if you've had lower tier phones. Well the few hours is so that you can A/B the other phone later and be slapped in the face lol. I wouldn't say that these are fart cannons at all though. 

Get four DJ100s. Do it. Just kidding, but get some Ultrasones.

I'm inclined to point you towards the Koss Ruk50. Yes I realize they're around 1/4th of your budget, yes I realize they look kind of dorky, and yes I realize that Koss has a stigma attached to them because they put out a lot of junk in the 1990s. None of that changes these being very good bassy cans, which provide acceptable isolation for mobile use, are comfortable, and will run straight out of your portable (the 1/8" plug, however, is not OtterCase friendly - it's kind of fat). And yes, they sound better than the Beats (at least the ones I've heard), are more comfortable, and cost considerably less. And did I mention the lifetime warranty? (Because that's also a thing with these). One thing worth considering - the Ruk50 do not come with a pouch or case, however the Bose TriPort/AE2 pouch is a perfect fit, and only costs $8.

Other suggestions, if you want a different aesthetic, would include the Creative Aurvana Live and Bose AE2. Both cost more, and provide a more "grown up" experience (looks, and sound). If you want a lot of bump in the trunk, the Ruk50 will go further towards that goal - if you want a more leveled out listening experience, the Creative and Bose are better candidates.

Regarding Ultrasone - my experience is more with their open headphones. I think both of them are stellar, but neither is appropriate for mobile use. The HFI-780 and DJ1 seem to be popular as closed-back models, but I have no opinion on their sound. Both fit into your price range though, and from specs should have no problem with your iPod.