If you're washing your hands prior to handling, that's not typically an issue. And the bag is more likely to already have contaminants on it.
The bigger issue is more you picking up something and transferring it to your other animals or yourself. This is why when you go to pet shops they typically have salmonella warnings posted around reptiles and birds or need to hand out literature about zoonotics. And why you should always be washing your hands after handling animals as well.
I say this as an immunocompromised individual who thankfully has never contracted salmonella from my reptiles, but have contracted psittacosis from birds
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