Reservation software to display on website

I’m building a website for a client that wants a reservation/booking service embed into the website for a transportation business. I chose not to use the e commerce platform and went with Calendly at first. The problem is that with Calendly people can’t chose the duration of the meeting. The second problem is that when a timeslot is booked nobody else can pick this time and date. Anyone who knows a replacement that solves these problems and doesn’t cost a fortune?