One of the cheapest and fastest way to travel from Cebu to Dumaguete (and vice versa) is via land trip to Liloan in Santander then a very short pumpboat or fastcraft ride to Sibulan port where one can get tricycles or multicabs for Dumaguete. These two images are the current schedules and fares of the two as of this posting date.
There’s also a roro from Samboan – Tampi (Sibulan) but I haven’t checked the schedules out.
Santander – Sibulan pumpboat schedule. Left two columns: first column refers to Sibulan wharf, second with Liloan wharf
Sibulan – Santander fastcraft schedule