Shy baby

My daughter will be 1 in a couple weeks. I didn’t take her out much over the winter since she was little and I figured what’s the point of bringing her to stores to be around germs when my hubby or mom could stay with her while I run to the store. Well now that the weather is nice I’m trying to take her out a lot and to socialize. But when people say hi to her and smile at her, she just stares at them and then rests her head down on me. She will let people hold her and she won’t scream, especially if I’m not in her sight. But as soon as she sees me she tries to get back to me. Is this normal? I know people say it’s weird and since I’m kind of reserved myself, they think “oh wow, her baby is standoffish just like her”. She really is a sweet and happy baby, just still getting used to new people. But is this normal or are most babies smiley and giggly when strangers talk to them/hold them?? First time mom here so I worry about everything :/