The reason you feel safer on your bike is because you likely have a good bit of experience on it. Once you reach a fair level of competence, you can control a bike quite precisely. Plus, when a bike is set up well for high speeds, it should track straight as an arrow. The gyro effect of the wheels and engine internals spinning at such a high rate keep it from being able to change directions too easily (or get out of shape).
By comparison, a car feels large and heavy. You just know that if anything ever got out of shape, there is little to no chance of saving it. They do not have the benefit of a natural gyro because they do not roll on an axis to change directions - the rear swerves from side to side and you're done.
Cars at high speeds have never felt as safe to me because they feel like they begin lifting off at very high speeds and start moving around a good bit. The bike is glued.
I don't agree overall.
But I would agree that a stock bike feels safer at high speed when accelerating, when compared to a stock Viper.
I would believe that is due to the time it takes to get there.
My Viper felt EASY at high speeds. Much better than bikes I have owned.
But it also got there faster than bikes I have owned and it was modded for high speeds. It felt more glued and tighter than a bike also.
So it may depend on what bike and or car in comparison.