Supply of Goods and Services or both to govt department, it can be a B2B or B2C, it's depends upon that department have a GSTIN(As Regular taxpayer, Not a TDS deductor) or not. If Department have GSTIN, than its B2B , otherwise it's B2C.
You may ask for the GSTIN from department or may even find it on the work order or contract paper or other documents/communication. If you find GSTN (as regular dealer) of Govt than you can do the billing accordingly.