There is not explicitly “Public” transportation to Mt St Helens from Seattle or Portland, however there are private tour companies that provide roundtrip excusions to St Helens from both Seattle and Portland. From Seattle, the trip is an all day activity with a good 6 hours spent on a bus going to and from St Helens (3 hours each way) The driver from Portland would be shorter but the trip is still a “day trip”

Greyline Tours

For average drive times to various locations at St Helens check this webpage St Helens Drive Times

The alternative would be to hook up with someone (trust worthy) who was headed down for a St. Helens visit to decrease cost and increase flexibility. (Alas, I have no currently scheduled trips yet for my Girl Scouts so… I can’t offer an alternative at this time.)