In order to be compliant with state and federal accessibility laws, all videos that are a form of official communication must be captioned for the deaf and hard-of-hearing.
Washington State discount
Washington State has form a contract with 3Play Media to receive a discounted rate for video captioning (and other) services. Currently it costs about $2 per minute of video captioned. When using 3Play, it is possible to send videos to their servers directly from the UW Bothell YouTube channel, and when they've completed captioning it, the video will update automatically with the new captions. UW Bothell departments are encouraged to set up their own account with 3Play Media. Please contact firstname.lastname@example.org with any questions on video captioning.
YouTube is a possibility if you're looking for free options. Users can type the captions into YouTube directly while listening to the audio. If the video is hosted on a channel that you do not have the login credentials for, you will need to contact the owner of that channel and work directly with them on a solution.