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Rome2Rio shows you a few options, including the company you found:
A bus with Bus SAS MK will take 12 hours and cost US$55-75
Bus Simeonidis takes two buses, to Thessaloniki and then on, for a total of just over 15 hours for US$85-115
Or as you've found, Bus Alpar Turizm goes for 15 hours and costs $80.
So you don't have to rely on just one company, and some of those (like Bus SAS MK) run 4 times a day.
As for timetables, my experience travelling makes me never rely on a timetable - it's merely a guide and to be treated as such ;)