Do buses run on May 1st in Bavaria?

Edit: As has been pointed out in the comment Ingolstadt Village is not the main stop for Ingolstadt but instead a shopping center - being an English speaker I had assumed incorrectly but should have checked. As far as I am aware nothing written below is incorrect, but some parts are not relevant.

You haven't listed the bus number in your question but as far as I can tell you are asking about the X109 (https://www.invg.de/maps_airport).

The timetable (https://www.invg.de/timetable_airport_express) contains the following notes for the stop Ingolstadt Village which Google translate translates to:

Towards airport: "For Ingolstadt Village applies: only Monday to Saturday, not on public holidays. Registration at least one hour before the desired departure sign up for information in the Village. The transport takes place via taxi or Minibus to the stop Kurt-Huber-Straße and from there continue with Airport Express to Munich Airport."

Leaving airport: "For Ingolstadt Village applies: only Monday to Saturday, not on public holidays. Passengers have to change at Kurt-Huber-Straße and From there you can take a taxi or minibus to Ingolstadt Village."

This to me implies that the rest of the bus route runs as normal on public holidays, but the connection to Ingolstadt Village does not run. So what you need to do may depend on how near another stop you are. Alternatively you could try and sort your own taxi or look at other bus services.

I want to stress that this answer is based entirely on what I could fine online, and anyone with any local knowledge or who knows otherwise should please feel free to write another correct answer.

I could confirm with the bus company that the bus to airport runs on May 1.

From Stadtbus Ingolstadt GmbH, I got an official answer:

Unser Fahrplan ist das ganze Jahr über gleich. Egal ob Feiertag, Samstag oder Sonntag.

which means that "Our timetable is the same all year round. No matter if holiday, Saturday or Sunday.".