What are the short purple bars on some of the trails? Does that mean you can't go on those?
Fallen trees across the trail that you can't hop over.
Travel beyond is permitted, but obstructed. (Not permitted would be a purple X across the trail, IIRC.)
So are you forced to 'bushwhack' with your mountain bike over your shoulder, uphill in some instances?
Definitely enhances the 'over or around' decision!
Some of them are also gated trails, which usually have pedestrian/bike pass-arounds which would force you to slow down, but not necessarily get off the bike.
The ones that I saw were just individual downed trees, so you'd need to get off the bike, lift it over the log, step over, and start riding again. A small delay, but enough to make a route choice versus a slightly longer unobstructed trail. I'd guess that a trail crew will clear them when they get a chance.
843 Dangerous object across tracks or paths, stairs
These barriers must be highly visible on the map and should be overprinted in purple. The symbol should be used for all obstacles that are difficult to cross. This symbol can be used for stairs. There is no particular stair symbol.