Yes, be very careful increasing the stock PSU voltage because the current through the bed heater (and the controller board assuming you are not using an external current booster) are quite high.
Merely increasing from 12.0 to 13.0 volts could increase the bed heater current from approximately 23.5 amps to around 27 amps.
At that point there is not enough output capacity remaining from the stock PSU (30 amps max) to power the hot end heater or the motors.
Aside from probably melting the connectors on the board which are only rated at 18 amps or so, the PSU will become erratic and could overheat, shut down or even go up in smoke.
Not to sound like a broken record, but if you haven't added an external current booster board for the bed heater, you need to do so if sticking with the stock PSU.
As Walter said, switching to a 24 volt or mains-powered bed heater would be a better solution.
I am currently installing a 500 watt 110V mains-powered bed heater in mine (but with our local mains voltage it will actually run closer to 600 watts) .
The stock heater is 300 watts if you can even get the full 12 volts to it considering wiring and switching losses.
There is a trick I used to do to help it heat faster that you might try.
Take several pieces of scrap typing paper and fold them in half lengthwise.
After homing the motions to the center of the bed, place one on each edge of the bed near (but not touching) the nozzle covering the open bed surface.
That will insulate it to some extent and help the bed to heat up faster.
Do NOT leave it unattended.
When the temperature gets up close to what you want it to be, say within 2-3C, remove them.
Don't worry about the paper catching fire because it auto-ignites at around 230-250C and the bed will reach a maximum of around 100C (if you are lucky).
But DO remove the paper before the nozzle begins to heat up.
Normally it won't heat up until the bed has reached its target temperature.
Others have done this in various ways using paper, rags, insulation foam (not styrofoam) and so forth.
I am not saying it is without risk, but at least until you can upgrade the bed heater it might help you out a little.
Do this at your own risk of course.