I’ve been on Mines a lot, sometimes to the Junction, more often to the top 5 miles short of the Junction, sometimes turning around earlier, almost always on a Saturday. Everything is relative, but I think Mines/San Antonio Valley Road from Livermore to the Junction is pretty safe. Traffic is quite light once you get past the Del Valle turnoff.
On a Saturday, once past the Del Valle turnoff, you’ll see more bikes and motorcycles than any other vehicles. You also might see the occasional parade of sports cars, or single sports cars. It is mostly joy riders out there on a Saturday, whether human powered or not, whether 2 wheels or more. The earlier in the day you go, the fewer motor vehicle joy riders (in the cold of winter, most cyclists don’t start too early, there can be icy patches early in the morning in winter, but as things warm up, most will get early starts to avoid the heat). The closer you are to Livermore, the more you’ll see vehicles going to or from ranch property, the occasional horse trailer, but there aren't that many properties out there, there can only be so many vehicles. Occasionally, there will be a Saturday morning where an event is starting at the Boy Scout camp around 14 miles from Tesla, and then you get some more SUV’s and Mini-vans on the road, but those vehicles tend to drive safely and slowly on a road they’re not used to that seems to them like a scary road to drive, and it never seems like a lot. There are stretches of one lane road, but mostly reasonably wide one lane (after all, if cars are coming the opposite direction from each other, they need room to pass). I feel safer on my bike in the one lane stretches than I do in my car.
Of course, you always hope nobody crazy is coming the other direction, but on any road with vehicles, you always hope nobody crazy or drunk comes your way. Full disclosure, awhile back, maybe 8 years ago, a solo rider on a weekday ride went missing. After a lot of searching, he was found off the road hidden by plants, dead, an apparent hit and run victim. I think he was around 15 or 16 miles south of Tesla. A couple of years ago, I was around 17 miles south of Tesla when a CHP patrol car passed me slowly, then eventually came back the other way, then passed me again then and back the other way again. I was worried he was looking for another missing bicyclist. As I came back towards Livermore, down around the 19 mile mark, the CHP car was parked by a tow truck that was trying to pull up a motorcycle that had gone off the road down towards the arroyo. The incident had happened awhile earlier and the rider had been OK enough to get someone to take him to a hospital. It does make one think, man, if that guy was so out of control that he couldn’t even keep himself on the road, what would happen if he had come upon a bicyclist?
In all my times up there, however, I’ve never had vehicles that scared me. I was riding Redwood Road last Saturday, and 3 or 4 sets of motorcyclists were being somewhat crazy and one pair especially scared the snot out of me worse than I’ve ever been scared by vehicles on Mines, as they took a right-hand curve really close to the right edge where I was riding.
With respect to non-traffic issues, I have been scared by animals going across the road in front of me, most notably a hare and a bobcat. Also, during a rainy winter, you may find a couple of spots where rocks spill out into the road, but not a danger if you're going uphill, and if I'm going downhill, I've seen them on the way up and know where to look for them and not ride too fast around the curves they are lurking behind. Of course, there are those who will ask, "What's a rainy winter?"
All I have is my personal experience, and based on that, I think traffic wise, Mines from Livermore to the Junction feels as safe as any route I ride. It is a fun ride.