She seemed very guarded

I just got back from a date with a girl I met on the internet, she seemed very guarded. closed body language, kept her bag between us when we walked so I couldn't take her hand. She also had half of a vanilla vodka coke with dinner. so either she decided the second she saw me for the first time that I'm not what she's looking for, or she's just very guarded around new people.

so assuming it's the latter, how do I put her more at ease around me?