There is a lever inside shutters that will slide into a notch when the shutter is set for B. If this lever doesn't slide into place, the shutter will do what you describe. This indicates that either a spring has broken or slipped, the lever itself has broken or slipped, or most likely that there is gummed up grease or dirt preventing it from moving into place. Most likely a simple cleaning will take care of it. Using for a while, moving the shutter dial back and forth, might also get it working. This and the slowish 1-sec. says that a cleaning would be nice. At the least, a warning to a buyer that it will need a cleaning.
This lever and notch, by the way, has only one function- for B. So it is very possible for just this function to be off while everything else gives at least some signs of life.
Paul Ebel does good work on Rolleis. Mark Hansen. Along with Fleenor and Krikor, of course. Closer to you, Seawood Camera in San Rafael might be worth contacting to see if they either do repairs or know of a repair place- Dead Link Removed they sell used Rolleis and check over older cameras. Whether to get it done or sell it as is is a difficult decision since getting it done right can cost enough that it is hard to recoup.
FYI, I overhauled this model, super clean but gummed up from no use, and sold it for $350 (inlcuding hood) in the Bay Area recently. Just to give an idea as you figure out costs, etc.