World Jump Day was a hoax (performance art), and wouldn't have worked anyway.
The only thing that could reach us from Betelgeuse is its radiation, in the form of starlight. No one would need to tell you about it, it would glow as bright as the full moon and be visible during the day. Shock waves exist in a medium, so cannot spread through a the vacuum of space, and the material of the nova itself slows down under its own gravity. Even if it didn't, it would take billions of years for any material to reach Earth, and by then it would be so dispersed that it would be indistinguishable from the background sprinkling of atoms that exists normally in the "vacuum" of space (a handful of atoms per square metre).
It's approximately 650 light-years away. Only supernovas closer than 50 light-years run the risk of irradiating terrestrial life on Earth, and there are no candidates.
Scraby's right about the possible wider orbit by the red giant phase. The sun will have lost about 30% of its mass as stellar wind and starlight, so will have less gravity, so the Earth may have entered a wider orbit. This still may not be enough, it'll probably orbit within the sun's own atmosphere, and the drag will slow the Earth down, causing it to spiral inward.
The interesting thing about red giants is their density. The sun itself will have grown from 1,361,000 kilometres in diameter to more than 300,000,000,000 kilometers in diameter, about 250 times. Yet it will consist of 0.7 solar masses.
Similarly, Betelgeuse is ~1180 times the size of the sun (as you saw in that delightful image earlier) yet only ~18–19 solar masses. That is on average significantly less dense than the uppermost atmosphere on Earth, and considering the size of its corona and atmosphere (which doesn't really have a defined terminator line) and the fact that it pulses in size and brightness regularly and asymmetrically means it is less of a spherical star and more of a hot cloud. Or a hot vacuum, effectively.
Oh, and in case you don't know which one Betegeuse is, it's this one:
It really is special to be able to look up at the night sky and be able to both locate and identify a particular star. "I know your name," you could say to yourself. "Beetlejuice, Beetlejuice, Beetlejuice!"