Date conflict using Event Picker

That would definitely be a nice basic function, but when you take into account timezones and overlapped durations it would certainly be super tricky.

So, the answer is you have to have a workaround, likely using a custom form.

The event picker will write to two user-specific columns the start time and end time. You would then have to use some further logic to determine whether they “overlap” with any of your existing bookings.