How to calm skittish pet rat who needs eye drops?

Hi there, my fianc� and I got a male rat just over a week ago from a local pet store. Columbus is 13 weeks old, and is very skittish of us. We are able to sometimes give him a treat by hand, but that's all. He will squeak and run away if we try to pick him up. He's bitten my fianc� a few times out of fear, once his teeth grazed the skin so it bled a bit. Normally I would happily take my time to get him to trust us and everything, but we had to take him to the vets last week because he looked like something was wrong with his eye, which turned out to be an eye infection, and we were given eye drops for him that we have to put in his eye once a day. Now my fianc� has left on a camp for the week, which leaves me to deal with the terrified rat by myself. He's very squirmy when I try to pick him up so often gets away. I'm wondering if there's a quick way for him to trust me enough to hold him and put the eye drops in? Thanks :)