Option 1: Take the metro to Milano Centrale and use one of the direct airport buses from there
I think your best public transport option is the one you already found: take the metro from Lampugnano to Centrale. Three options are available (ordered by simplicity in terms of changes, and shortest route in terms of number of stops):
- M1 (red) from Lampugnano to Cadorna, change for the M2 (green) and get off at Centrale
- M1 (red) from Lampugnano to Duomo, change for the M3 (yellow) and get off at Centrale
- M1 (red) from Lampugnano to Lotto, change for the M5 (lilac), go to Garibaldi, change for the M2 (green) and get off at Centrale
ATM's very own planner (GiroMilano) says that journey number 2 will take you approximately 29 minutes including changes and walking upstairs to Milano Centrale train station:
From Milano Centrale you have a Orio Shuttle bus leaving at 11:20. With an expected journey time of 50 minutes + optional 20 minutes for delays, you should make it to the airport before 13:00. If you miss the 11:20 bus there's one at 12:00 which should drop you at the airport before 13:30. Similarly, the Autostradale bus leaves from Centrale at 11:35 and 12:05.
Option 2: Buses departing from Lampugnano or nearby
Now you asked for information on buses serving the Lampugnano - BGY Airport route.
SAJ-Operated Bus from Lampugnano to BGY
You already found the one run by STJ, whose timings are not compatible with your journey. Let's mention it here nevertheless. The bus runs from Milano Lampugnano to Udine (Friuli-Venezia Giulia, Italy) stopping at Orio al Serio Airport on the way. Two daily departures are scheduled at 14:30 and 17:30. The bus does not run on Sundays nor during holidays:
Two-Bus Combination from Lampugnano to BGY
Rome2Rio also suggests a two-bus combination from Milano Lampugnano to BGY. Autostradale and Nord-Est Trasporti run frequent daily buses covering the Milano Lampugnano - Bergamo FS (train station) routes. The journey time is approximately 50 minutes with several stops on the way. The Autostradale bus is line 44 serving the Milan - Grado journey, with a few departures per day, and even fewer on the weekends. The Nord-Est Trasporti bus is the Z301 line with detailed departure times and stop lists showing several departures per day and a more than decent coverage during the weekend. At a quick glance I'd opt for the latter.
Once you get to Bergamo FS you'll have to jump on the Bergamo ATB Airport Bus to Orio al Serio Airport.
Below is a screenshot of the Rome2Rio journey:
Autostradale- and OrioShuttle-operated Bus from Fiera Milano Rho to BGY
Both Autostradale and OrioShuttle run buses from Fiera Milano Rho to Orio al Serio airport. The caveat is that these buses run only on days in which there are scheduled fair events at the Fiera Milano. Their departure times from Fiera Milano Rho are late in the afternoon, so as to be compatible to when people leave the fair and exhibitions.
To get to Fiera Milano Rho you'll have to take the M1 (red) from Lampugnano and go all the way to the terminal station called Rho Fieramilano. You'll need an extra-urban ticket for this journey. Tickets can be purchased in all metro stations.
For completeness sake, here are all the bus services going to/departing from Orio al Serio Airport.