There are buses to Dallas from the North & South remote parking lots, but it's a major schlep. There's a trip planner at dart.org you can try. Try using CBD West Transit Center as your downtown destination. I'd allow a half hour after you clear customs due to the wait for thefree airport shuttle to the parking lot.

What I found was a 7:29 bus from the South lot (route #408), a 15 minute transfer at Mockingbird & Harry Hines to the #44, arriving downtown at 9:15 am. I'd hate to do that after a long overnight flight, myself.

If you really want to get downtown, I'd suggest a cab ($45 flat rate), Supershuttle, or trying for a cheap rental car using Priceline.