Modals (popup content) present difficult accessibility challenges. In the past, the way I’ve done it is to save where the current focus is before a modal is opened, inject the focus into the modal, then return the focus to that place after the modal is closed.
That still doesn’t solve the problem when a user tabs out of the modal. THey’ll often end up dropped somewhere they don’t want to be in the page. To solve that problem, I add hidden, focusable elements at the top and bottom of a modal. When a user hits these, it bumps them back to the other end of the modal so they can’t escape it.
Of course, then you have to make sure the user can close the modal from within it or they’ll be trapped forever.
As I said, it gets pretty complicated. The most I’ll probably do for the date and time pickers is to restore the focus to the booking form when they’re closed.