Does the amount that I paid on my student loan last year for a bachelors degree count toward the college tuition tax break for NYS?

No, the NY State college tuition credit is just for college tuition.

NY State College tuition credit or itemized deduction

Who is eligible? 

You are entitled to this credit or deduction if:

• you were a full-year New York State resident,
• you, your spouse, or dependent (for whom you have taken an exemption) were an undergraduate student who was enrolled at or attended an institution of higher education and paid qualified tuition expenses, and
• the student is not claimed as a dependent on another person's tax return.

Qualified tuition expenses

• Qualified tuition expenses include only tuition paid for the undergraduate enrollment or attendance of the student at an institution of higher education. This includes expenses paid from a qualified state tuition program (like New York's 529 College Savings Program).
• Qualified tuition expenses do not include:
  • tuition paid through scholarships or other financial aid that need not be repaid
  • amounts paid for room and board, and other similar personal or living expenses
  • amounts paid for books, equipment, and activities, even if required by the school