Re:Gauging interest in a Northern Rockies M&G 6 Months, 2 Weeks ago
Probably July and August would be best. June is typically our rainiest month. But that varies.
If we do the Beartooth highway then I think it would have to be late July or August. It opens as early as Memorial Day, but it can be hazardous for motorcycles through June. At that elevation the snow berms are still melting over the roadways and can freeze overnight. But they say to always bring gear for rain. At 10k+ feet you can get weather any time of the year.
The downside is that hotels in that are pretty expensive that time of year. And they sell out fast. Red Lodge is on the East side of the highway, and Cooke City to the West . I just looked at Expedia for July 26th, 2018. Only 3 hotels aren't booked and they are $110-$140 per night.
Another option would be to meet up in Billings. 60 mile ride from Red Lodge, but much easier to find lodging at a better price.