No.
First, mountain bikes are not permitted in wilderness areas.
So, it appears that you are not aware of wilderness areas or regulations.
Second, although dogs are not prohibited in wilderness areas, they can be problematic.
Spooking horses, chasing wildlife that have a very short summer feeding season.
And they can attract bears, wolves, and mountain lions who see them as dinner.
http://missoulian.com/news/local/mountain-lion-reportedly-kills-dog-in-grant-creek-area-fwp/article_add3439c-bce7-5f46-943d-0f7b375c9015.htmlThird, most national parks and wildlife areas have strict leash requirements.
You may be ticketed and removed from the premises if riding with an unleashed dog.
Some wildlife areas ban dogs altogether except for service animals.
Fourth, ranchers shoot dogs that chase their livestock. No questions asked.
Dogs that separate calves from cows and chase livestock are seen as pests.
The law is on the ranchers' side.
I've lived, hiked, biked Wyoming & Montana for 30 years.
Most dogs can't run 50 to 75 miles per day. 25 is the experience of one couple with their dogs.
If you did bring your dog, you would need a dog trailer for the downhills and the flats.
I've ridden the backcountry with folks who have dogs. Cut your mileage 25%.
Just leave Fido with Aunt Sarah.
PS - 75 miles is really pushing it on the GDMBR even without a dog.