'taking out road vibration' is a bit of a red herring. You hit a bump, the bike (and the saddle) goes up. You hit a hole, the bike (and the saddle) goes down. You go over a 'knobbly' surface the bike (and the saddle) goes up and down.
What's interesting is what happens after that. Aluminium resonates or 'judders'. Carbon doesn't - or, at least, not nearly as much. So a carbon bike, or a bike with bits of carbon, will be less wearing on the wrists and bottom.
Tyre pressure and width is a bit more complicated than 'soft is comfortable'. Your body will take less of a bashing if your tyres are soft - but, then again, the bike will be more wobbly, and you will expend more energy propelling it along. That might be harder on your wrists and hips in the long run. I ride all day on 120psi. More to the point, so does Susie, who is a size 10, 52 years old (now I have to kill you all) and not a particularly strong cyclist
As ever, though, the difficulty is in the question. If your bottom hurts....why does it hurt? Because it's getting bounced around, or because the distribution of your weight is wrong? If more of your weight was going through the pedals, would your bottom hurt? If you're of average weight you shouldn't really be putting so much weight on your bottom that it hurts. If you're of above average weight then life's more difficult.