I'm not even clear on how you could reasonably bill hourly for on-site work. Your client made you travel to their office and then back. Your day is shot; your client ate the whole thing up. They pay for a day.
The universal convention in the US is that a work-day is 8 hours long. You don't need to spell that out (doing so just invites questions and unwelcome negotiation). Work an 8-hour day. If your client has a problem with that, they'll tell you, and then you can negotiate. That negotiation may end up with your rate jumping up (GREAT: that's your new rate there forever), or with you jettisoning the client.
The universal convention in the US is that a work-day is 8 hours long. You don't need to spell that out (doing so just invites questions and unwelcome negotiation). Work an 8-hour day. If your client has a problem with that, they'll tell you, and then you can negotiate. That negotiation may end up with your rate jumping up (GREAT: that's your new rate there forever), or with you jettisoning the client.