This trip is possible only by regional train. All regional train rides in Germany are the same when it comes to getting a seat, no matter what ticket you use - there is no reserved seating. Regional trains might travel very long distances, but they fall into the same general category of transportation as buses, trams, and subways. You buy a ticket, then you get on and look for a seat.
There is zero advantage for early purchase when it comes to regional-train-only journeys. The Bayern Ticket is non-refundable if your plans change. So just buy it on the 23rd, or on the 22nd for the date of the 23rd.
The Bayern Ticket covers regional trains and buses too - so after your train trip, the bus trip to the ticket office area is covered by the Bayern Ticket also. You are traveling on a weekday, so you may not use the Bayern Ticket until 9 am. The Bayern Ticket is more than a ticket - it's a day pass, so it's valid for the trip back to Munich, and it's also valid for any additional trips you might need to take within Munich or outside Munich on that same day, as long as your travel keeps you within Bayern (Bavaria.)