Is there really nothing though? Would some kind of a bunker not help? Like imagine 50m-100m underground? Not sure how much matter it might take to stop fast-moving particles (or all the dangerous forms of associated radiation).
It would not be difficult. Nuclear reactors could provide power almost indefinitely. Greenhouses could maintain plant life. Animals could be bred and slaughtered. A quick survey would have to be made of all the suitable mine sites in the country, but I shouldn't be surprised if several hundred thousand of our people could be accommodated. Every nation would undoubtedly follow suit.
There is no risk for the Earth due to Betelgeuse. At worst, space travel will be impacted, but we would have 100k years to prepare for that after it blows up.