2nd half of July and August are typically dry around here. Not that it won't rain but even when it does the rain does not hang around for long.
For Mountain Bike rides, check out the Evergreen Mountain Bike Alliance -
Evergreen Mountain Bike Alliance - Washington's Largest Mountain Bike Club
A couple other MTB opportunities:
If you are into Enduro Racing, the Cascadia Dirt Cup series is a ton of fun. The Rainier Enduro is a new add to the series this year and is going to be an epic day, but they are all great events -
Cascadia Dirt Cup*|*
If you want some epic backcountry rides, join one of the the Washington Endurance Series rides-
Washington Endurance Series | Inspiring people to go on epic mountain bike rides in the Evergreen State