It sounds like this is a configuration in your Jira project and is nothing to do with Zephyr. I'm guessing that whoever created the Bug issue type has made the Resolution a Required field - not always a simple thing to do.
The way to solve it would be to ask your Jira administrator for help - they may create a new issue type for you or fix the Required field in the existing Bug issue type.
So I am the administrator and setting up Jira and connecting Zephyr Squad, etc. There is a required field on the bug but only when it is being set to closed. No where else on the bug is the resolution field required. Whats more interesting is that issue and Task also have the same requried resolution field set. But they are not being triggered to enter a resolution from creating an issue in zephyr Squad.