I've road all 4 entrances in the park. I've been there 3 times. Always the week before or the week after Sturgis.I love riding the park and surrounding areas. I've hit traffic a few times. Its never been bad enough to keep me going back. I always found the earlier you head out the less traffic you got into. I'd love to go back this year.
Take a wide variety of clothes. Be prepared for cold and rain. As others have said make reservations early and take plenty of cash.
Have fun and enjoy.

 

Don't follow a car into a buffalo herd. The car will stop in the middle to take pictures and leave you sitting unprotected.

 

Buffalo herd will stop cars along the way..
Don't be the guy on a bike getting attacked by one of them..shut your bike off!

 

I have sat on my bike a few times when they where crossing the road. One was about 10 ft from me, stopped, looked at me for a minute, then moved on. It was pretty cool.

 

In August 2014, I camped at Canyon. Every morning when I got up it was 30 degrees. I would leave out in full leather and be in a SS T shirt by about 9:00.

 

Traffic will be heavy, but you will be looking at lots of stuff, so not a big problem. HOWEVER.. In July I passed through Gardiner headed north. and I could find no motels anyplace....was headed back to Seattle, and ended up going all the way to SPOKANE, WA. before finding a motel. It seems that all of Wyoming and Montana are the place to be on vacation that time of year.
Have a great trip... ride safe....

 

Beartooth, Chief Joseph Hwy is an awesome ride. And anywhere around Cody and Jackson Hole is great. I personally prefer to stay out of YS on my bike, because of the slow stop and go traffic. But if you get through without a lot of stops in the traffic, YS would be beautiful on a bike.

As someone else mentioned. Be prepared for all different weather. When we rode bear tooth if got down to about 34-36 degrees on top and was about 75 in cody.

 

Looks like your question has been answered but I'll chime in anyway. The road from Cooke City to Gardiner, as others have said, doesn't have a ton of traffic, but it can still back up. There are places to stay in Gardiner and it's got a cool vibe that I like better than West Yellowstone. If you need to, Livingston is only about an hour north and it's a great ride along the Yellowstone River to get there.

The last time I was in Mammoth (on the way to Gardiner) there were a lot fewer elk than in years past. Some have blamed the reintroduction of the wolf.

 

"Livingston is about 1 hour north" ..and Nicks cycle shop is there

 

We were there a couple of years ago on July 3-4, and I was seriously stressed about traffic. Turned out to be a complete non-issue. We got into the park early. Maybe we were ahead of a lot of people who were going the direction we were (counter-clockwise from the southern part of the park). I don't know - but we had no problems. Enjoy. One of the best places we've been on the scooter. Going back this year on our way to the Canadian Rockies. Can't wait. Is it June yet???