Your car will be just fine with either approach as long as you slow down to a reasonable speed before hitting the speed bump, and so long as your car doesn't bottom out (bottoming out meaning some part of the car other than the tires touches the ground).
The kinds of stresses put on a car by driving slowly over a speed bump are no more severe than the kinds of stresses that the car experiences while driving around town (around corners, over small bumps, etc).
The most common damage caused by speed bumps is damage from bottoming out. The parts of cars that typically get the worst of this damage are the plastic bits down low on the front of the car (front spoiler, belly pan), or low-hanging parts of the engine (oil pan) or exhaust. Bottoming out happens when you drive too fast, and the springs of the car can't lift the mass of the vehicle out of the way of the road quickly enough.
Approaching the bump at an angle (one wheel at a time) would make it more likely that you would bottom out, as you're then asking only one spring to do the job of lifting the car clear of the bump, instead of having two springs work together by approaching the bump straight-on.
In short, just slow down. If it doesn't sound or feel abrupt/violent, the car will be just fine.