While you do not need an ESTA, you can get one. Last time I crossed a Canada/US border, by car (no need of ESTA either), the border agent asked me if I had an ESTA. When I said I thought I did not need one, he told me the process would be faster.
But most importantly, there is a priori no reason you will take much more time than most other travellers. As you said, the total processing time for the whole bus is around 30-60 minutes. Depending on the number of people crossing the border (probably higher around holidays and maybe Friday and Sunday nights), there might be some more waiting in the bus, or fewer border agents. The process for a "VWP citizen" is a few questions on what you plan to do in the US, the filling of the I-94W, the green paper with your identification and a few questions, and the payment of 6 dollars by cash (USD only) or credit card. That does not take much longer than for other passengers.
If for some reason, be it you carry forbidden merchandise, or you are considered a threat, or whatever, they may keep you for longer. That probably does not happen to more than 1 or 2 people in a few buses (I have crossed the border by bus a couple times and I saw that once or twice, including once at the Canadian border). In that case missing your bus is probably the biggest worry (it is more the fact that you may not enter the US). I wondered like you what happens. In my opinion (I never tried!) you can either take a later bus, if there is a free spot. Regarding air travel, carriers take responsibility of transporting the people banned from entering the US back to their origin, so I suppose Greyhound should also bring you back to Vancouver if you are denied entry (or get you to Seattle if eventually allowed). Or you may be allowed to call a cab to go to a border town (on either side, depending if you are allowed in) and then you'll be able to board a bus there. Anyway, this happens often enough so that the border agents probably have a procedure for such people.
So in any case, you should not worry too much. Make the process as fast as possible, by thinking of where you go in the US, what is the purpose of your trip, by having a ticket to leave the US (by land or air or sea), a proof you reside outside the US (or even a pen to fill the form). You can also get an ESTA if you are very worried. And if for some reason the border agents decide to keep you for deeper investigation, when they release you, they probably have a procedure for that purpose.