What is the quickest way to get from Milan to Siena? Is there a direct route? I am wanting to go Wednesday, May 22, 2019.
Look at Rome2Rio: https://www.rome2rio.com/map/Milan/Siena
I don't see a direct train. There always seems to be a change in Florence, and often a second change as well. Travel time can be as little as 3-1/4 hours but can also be quite a bit longer.
You can check your options here: https://www.trenitalia.com/tcom-en.
You will be traveling from Milano Centrale to Siena.
I would be extremely cautious about using Rome2Rio.com. It's good for telling you what modes of transportation are available between two cities, but it has proven to be extremely inaccurate about travel times, fares and frequencies. For that you'll need to dig down on Rome2Rio until you find a link to the website of the company operating the train or bus you're interested in.
It may make sense to travel from Milan to Florence by train and switch to a bus to Siena (buses Florence > Siena take a more direct route than the train and stop in the centre of Siena).
This advice is good as long as the bus station in Florence is close to the railway station - it is in via S. Caterina da Siena, so two minutes walking. But it the future the bus station could be moved away to ease congestion in the station area - in this case, train Florence >Siena could become competitive in travel time.
There is also an unfrequent minibus service named "Freccialink" that leaves from the train station in Florence, it is run by Trenitalia and tickets are issued together with fast train tickets. It may be the closest thing to a direct service - still one switch in Florence. You can find this option in the Trenitalia timetable.