You’re coming from a Schengen country into Munich and departing to a non-Schengen but EU country. Your itinerary consists only of Star Alliance flights (Adria Airways and Lufthansa). This means that you will be arriving at and departing from terminal 2 which is used exclusively by Lufthansa and its Star Alliance partners. You will need to clear exit immigration at Munich as your destination is non-Schengen.
Your general walkthrough will be:
arrive at Munich, terminal 2, Schengen area. You will be dumped in the general arrival/departure area as there is no need for additional security screening or incoming immigration. Depending on your flight, you may likely arrive at a bus gate or in the satellite terminal (you can tell by the arrival gate letter; G gates are in the main terminal while K or J gates arrive at the satellite).
make your way to the centre of the main building of terminal 2. In the best case, it will be a 10 second walk from one of the central gates; worst case scenario is probably a bus gate arriving at the outer end of the main terminal which is just one long line of gates. Still, depending on your walking speed you can probably get from the far end to the middle in five minutes or less.
Locate the path upstairs to the non-Schengen storey. I know there are stairs right after the main security checkpoint (which you would only see from the inside). I am unsure if there are any others; but there should be signs pointing you to non-Schengen connections in one way or another. Once you are upstairs, you will go through immigration control so have your passport ready.
Locate your departure gate. The numbers are the same as for the Schengen gates but the letter is H (main terminal) or L (satellite terminal). If you paid attention on your way in, you will probably immediately know which way to go but of course there is ample signage.
Board your plane.
Your US passport allows you to visit all EU countries for 90 days out of 180 days so assuming your trip isn’t extremely long that will be no problem and just a routine inspection. Security is not necessary as you are coming from an EU country and departing to an EU country (same for a potential return trip, btw).
All in all, how long this process will be depends on your walking speed, the gates you arrive at and depart from and the queues at immigration. But 45 minutes should be perfectly doable.
I just checked today’s departures and arrivals. The flights from Ljubljana are given as arriving at remote gates (i.e. bus gates) while the flights to Bucharest are noted as being H gates (i.e. main terminal).