fastest way to get from Gurye-> Busan Haeundae?

Hi! For context I have a skin appointment near Haeundae at 230pm and I'd be travelling from Gurye on that day. I tried searching on Naver, there seems to be a direct bus but I can't seem to search up the timings anywhere.

Whats the best way to ensure I can get to Haeundae by 1pm, drop off the luggages, have a quick lunch before the treatment? Transit at Suncheon? Thanks!