Just got back from Mammoth and it's an absolutely awesome sports mecca.

My first recommendation bike-wise would definitely be a mtn bike, which you could always easily rent if you decide to.

You could ride your CX bike on the various fireroads on the outskirts of town, but I think you may like the road bike better. There's a beautiful loop road (Mammoth Scenic Loop) with nice rolling hills, wide bike lane, and good pavement. Would be more fun on road bike vs TT bike, in part due to the wind (it's been clear but pretty breezy there lately.)

Also, if you're looking for other sporting pursuits, the ski mtn is open until Aug and has tons of snow still. Waterskiing/wakeboarding/etc on nearby Crowley Lake is also awesome (there are outfits you can contact to take you out on a boat).

Have fun!

I spent 8 weeks in Mammoth training. PM me and I can provide some routes for your road bike or TT bike.

Going up this weekend as well, wife's family has a place so i've ridden all of my frames. I'd take road if you can't take the MTB. Ride up past mammoth mtn to the Minaret Vista overlook over the san joaquin river valley (assuming the road above the lifts is open). Ride up Lake Mary Road to Horseshoe, there's even a bike path there now. Both good climbing and the altitude will leave you breathless :) For flats, ride down to the Green Church and out Benton Crossing Road around Crowley.

But I am bringing my mtb

Bring the road bike, and ride up to and around June Lake. If you are feeling really frisky, ride up Tioga Pass. Also, as someone else posted, there are routes out by Green Church that are good. I rode a big loop through there that comes out by Mono Lake.

Bring the road bike, rent a mtb if the itch needs scratching.

Last I heard Tioga Pass is closed due to the massive snow year but is supposed to open soon

Opened this week