Moonbase inhabitants (shielded by lunar soil) will be watching solar weather reports more carefully than a Midwestern farmer watches the weather forecasts.

With the current satellites and other technology, what's the warning time for a flare? What systems could be put in place to improve it? Fortunately nasty flare particles travel slower than light.

Charged particles could theoretically be deflected/absorbed by powerful magnetic fields (that's what shields us on Earth), but making this mobile enough for a moon rover would be a non-trivial problem.

I still say best bet for lunar bases is finding uncollapsed lava tubes and putting inflatables inside. Advantage--very little construction work involved. Disadvantage--such tubes may be few and far between (the existence of such tubes has been proven) and it's likely they won't be where you really want your base to be.

Think of it as a short-term solution, like our ancestors using existing caves before they had what it took to make buildings.