She asked if I could ask for citizenship, but I wasn't sure hence I asked here

You need ILR first. Not sure how long you have lived in the UK or what route you plan to take to ILR.
So, if I get married this year and ask for a ILR,
You cannot 'ask' for ILR. You have to apply and pay the large fee IF you meet the requirements. Not sure what your full UK immigration history, as you don't state this. Simply marry a British citizen does NOT give you any automatic rights for Immigration purposes.
when could I ask for citizenship...
Again, you don't 'ask' for citizenship. You have to APPLY and pay the fees when you qualify.
Would my years as an student count as part of these 3 years requirement?
Read my answer I have given above. I clearly stated it is being married to a BC at the time YOU apply. Nationality law says that this route under Section 6(2) of the nationality is based on 3 years residence. It does not state that it MUST be 3 years married to a British citizen. You simply need to meet the residence requirement, which is a separate requirement regardless of what visas you have held.