well I'd recommend Sennheiser HD 598, the Beyerdynamics, or AKG k242HDs...umm differences I guess:
First of all the Beyerdynamic 770s are closed, so forget about those. The 880s are probably a little out of your price range unless you go used. You can probably find a pair on eebay. My friend has a pair of them. They have a beautiful sound-stage and clarity, and they have enough bass, but their focus is more on the upper mids/highs (they're amazing for vocals/jazz/classical). One thing to be careful if you choose to buy the BD 880s: DON'T GET HIGH OHM ONES. I think they come in 32 Ohm, 80 Ohm, 250 Ohm, and 600 Ohm. You will NEED an amplifier for 250/600 ohm, 80 ohm will drain kinda drain your battery, 32 ohm would be ideal for your needs I imagine.
The 598s are probably your best bet. They're a little warm, good mids, wide sound-stage, bass is probably around on par with the 880s. Cheaper than the 880s. Not as comfortable. The 880s, while a little tight, have the softest velvety earpads. They kinda get warm after awhile though. The 598s are still pretty comfortable.
I have the AKGs, but I don't think the K242HDs are in production anymore. While the BDs have a boost in the upper mids/highs, and the 598s have a boost in the mids, the AKGs tend towards neutrality (meaning the mastering and mixing done on your track is what comes through. That or the eq on your player). They're not as comfortable, and they're pretty big, but I think they sound perfect for me.
So, I'd say go for the 598s. There are tons of other phones out there. I'd recommend asking on head-fi.org. There's a headphone forum where a bunch of audiophiles just talk about tone all day. I spent 3 days straight researching that website/searching the headphones I found there before I picked mine. It can get really specific when you start to understand exactly what tone you're looking for.
Also, since you go mountain riding, you might want to look at inner-ear monitors. Headphones seem really clunky for biking. I'm not sure if you can get IEMs that don't cancel noise though. I could go on for awhile about this topic, obviously. Just go to head-fi.org lol