The info below is from the DC Metro's web site. I take my dog in her bike basket since it has a strap that hooks through her harness and she can't get out of the basket unless I release her. I also print out the page from the web site and take it with me...just in case Metro employees are not aware of this policy.
Metro - About Metro - Q & A About Metro "Can I bring my dog on Metrorail and Metrobus?
The only animals that are permitted on Metrorail are service animals that assist people with disabilities. Pets are not permitted to ride Metrobus or Metrorail. However, a pet can be transported on Metrorail and Metrobus in a secure container as long as there is no possibility that the pet can get free."