It's not possible for a gamma ray burst to 'screw' the entire solar system. It's already an incredibly unlikely event to occur near enough to do damage. Then the beam would have to be directed in our direction. And the beam would have to essentially hit the solar system edge on or face on, but not at any other angle.

Even if all that happened, underground bases would be protected, as would above-ground or in-space habitats that happened to be protected either by the mass of the body they're on by virtue of 'facing away' from the GRB; or by virtue of being behind another body (e.g. Jupiter, the sun, some body they are orbitting) relative to the GRB. With space habitats, they may also be protected by virtue of already needing some level of protection against cosmic radiation; but that's highly speculative.

A GRB also wouldn't destroy the Earth. It would do a lot of damage to its ecosystems, but the Earth would be relatively safe again not terribly long after the event, even without human intervention. If we had the technology to colonize space, we could definitely recolonize the Earth, even in a worst case scenario where the entire ecosystem collapses.

How long would such a burst be expected to last? Because at least momentarily, one half of the earth will remain pretty safe.

Most of them are very short lived (think seconds at most), but they can be as long as a few hours. No part of the Earth will really be 'safe' for humans in sense of 'unaffected' like other places could be, but yeah, lots of people would only suffer from the after effects.