Homicide and Assault detectives are handling the investigation. Traffic downtown is understandably snarled; SDOT says to avoid Second Avenue and use First or Third. Follow the SPD's Twitter feed if you want updates as they happen, and we'll update this post when we get more information.
UPDATE: SPD says streets are closed in a three-block radius around the scene at Second and Seneca and to "expect street closures for at least 8 hours."
UPDATE 2 11:39 a.m.: Updates from the SPD blotter:
The male suspect reportedly stayed on the bus for a short time after the shooting, before he fled on foot through downtown.
Officers then spotted the suspect near 2nd Avenue and Seneca, where he opened fire on officers and ran to a second bus.
When the suspect tried to get on a second bus, the driver and passengers evacuated the bus and the suspect got on board.
Officers confronted the suspect on the second bus and shot the suspect.
UPDATE 3 4:36 p.m.: SPD confirms that the suspect has died. They've also released more information that includes what led up to the shooting:
The incident... began [at] 8:45 AM when three men climbed aboard a #27 Metro bus through the back door near 3rd Avenue and Union Street.
When the bus driver told the men to come to the front of the bus and pay, two of the men exited the bus.
The third man walked up to the front, where he attacked and then shot the driver.
A couple more photos from this morning are after the jump.