Let's look at some of the past missions to get an idea. In particular, let's look at the Echostar 105 mission. The mission launched on October 11. It arrived in port on October 15th. Unloading the booster takes less thenthan a day. There is some amount of time to refurbish, and then the ship goes back out for the next mission. It then could take about the same amount of time to leave. So the lower limit is a week.
The upper limit can be done by seeing how long between missions. The closest pair I believe was the Oct 11/ Oct 30 2017 landings, with only 19 days apart.
I suspect it could be done faster if required, but 1 to 3 weeks seems to be the fastest turnaround, if there aren't any issues with the landing.