Don't count on CCTA. One evening I got stuck in Essex when the last two runs were missed. I guess 5% of CCTA's operators were sick.
Before I get started, for full disclosure, I work for CCTA.
I'm not sure when your experience occurred, but it had to have been before the middle of 2007, when I started working for the authority. I can't speak for anything prior to that time, but I can't imagine that happening, at least based on my experience. In a worst case scenario, they will assign a supervisor to drive the bus. I've been riding the system for six years and while there are occasionally delays and infrequent cancelations, it's generally a very reliable system. Reliable enough that I don't need to own a car here (though I live right in Burlington, I would not say they same thing for most of the surrounding suburbs).
I take the bus from Amtrak all the time, provided you are coming in Monday-Friday, it works great, unless the train is over an hour and a half late, which is very rare. If you are interested in taking the bus and have concerns, PM me and I am happy to give you my personal cell number.
That being said, if you have a lot of bags and just want a hassle free experience, call Green Cab at 802-316-0700. They are the cheapest and best taxi service in the area and they will meet you at the station. There will be cabs at the station, but they are typically much pricer. The fare to Burlington shouldn't run more than $16-$17 depending on where you are going.
If you have any questions about what to do, where to eat, or how to get around Burlington, just let me know. I've lived here for six and a half years and am always happy to point visitors in the right direction.
I think there is a bus of some sort from Burlington to Plattsburgh, but I'm not sure of the schedule...
Unfortunately, there is no bus to Plattsburgh, or any good way to get from Burlington to there without driving.