The good news is that public transport isn't too bad, but realistically you have to travel to Garmisch-Partenkirchen the day before, so you can start early in the morning. Getting back to Munich very late is no problem. The Deutsche Bahn
gives all the necessary information (the German name for Munich is München).
I don't have personal information about current conditions specific to the Zugspitze area, but the ski season is just over, and early May there is always still a whole lot of snow higher up everywhere in the Alps. Even if someone has been kind enough to break trail, which would surprise me, planning to hike up and down to the summit in a day is very optimistic, to put it mildly.
The only feasible hiking route this early in the season would be the Reintal route
. In addition to the more than 2000m altitude gain, there is also the distance to factor in. It's been a few years since I hiked there, so I can't say how long exactly it is, but, for the most part, I remember that it's not steep at all - which makes it a very long hike.
Later in the season, when there is less snow, there are several alternative routes to the summit. One of those is the Höllental route
, steeper and therefore shorter, but that's not just hiking anymore. If I would want to climb Zugspitze in a day, that's the route I would want to take on the way up. On the descent I would follow the Reintal. But, frankly, I would rather take more time for it though - in fact, that's more or less what I did, back in 2007.
It's dark right now, but during day time you can check out the web cams:http://www.zugspitze.de/en/aktuell/wetter/panoramakameras.htm
The good thing is that if you end up being slower than anticipated and still get to the summit, but somewhat later than planned, you can take the cable car down (assuming that it is running - best to check the time table beforehand).
If you forget about hiking and the cable car to the summit is indeed operating, that's a much easier way to the top. To be precise, the cable car goes almost to the summit, but not quite, fortunately - there is still a short, easy climb left, but it's quite exposed and therefore virtually nobody coming up by cable car wants to do it. Obviously, if there is snow on that final ridge it's more hazardous.