Hi @Bob-And-Becky0,
You easily can set up to recieve booking requests and inquiries if you go to ACCOUNT - Notifications - Email Settings, then tick "Reservation and Review reminders".
You also can log in to your Airbnb Account once or better twice a day and then any new messges, inquiries, booking requests etc. will pop up, this is what I usually do when I am on travel.
In case you don't have internet access for some particular days at all, you also can change the status of your listing from "Listed" to "Snoozed" and set the time frame for the snooze function. This way your listing is not visible at all for the defined period.