Couldn't tell you the duration, but the marriott webpage pegs the taxi from the airport to that hotel (which is 1.2 miles from the conv center or something) at $42.50.
Or you can take the transit for $3.50, apparently.
In larger cities, the big hotels will usually have some sort of (pay-for) shuttle service to/from the airport, at the very least. If you've already booked your hotel, call them up and see if they have a shuttle available.
Sometimes you can also higher a bus service, I remember in Hawii I payed $50 for a taxi going out but got together with about 5 other guys and spent $12 going back on a bus.
I found this cool MetroLink thing that runs from the Airport straight to the America's Center (for those staying at a hotel across from it).
It leaves from the airport every 20 minutes, and takes 30 minutes to get there. You buy a ticket a TVM (machine). It only costs around $2-3 for a ticket.
If you want to go cheap, MetroLink is definitely the way to go. I live in a suburb west of St. Louis and we sometimes take it into the city from a stop near the airport. Very easy to use and cheap. 30 minutes sounds about right...