Using the attached example, you could use column B for your list of dates in a choice component, then once a date is selected, use a filter to filter times on True/False availability and Selected Date.
Unfortunately you may have to set up these formulas for each individual barber. Otherwise the transpose formula gets too large for google sheets to handle since with only 5 barbers, you would have a combination of 1960 available reservations over a 2 week period.