KiCad Bus on multiple sheets - Are labels the right way to go?
Is my bus now connected correctly, or am I using the idea of labels
  wrong?
  


Local labels (in your example, these are LED1, LED2) will all be connected.  So in your first image, the pin for LED1_0 and LED2_0 will be connected.  This is probably not what you want.  You should prefix each wire in a bus with the same string.  So ETH1_LED1 and ETH1_LED2 for bus ETH1 and ETH2_LED1 and ETH2_LED2 for bus ETH2.


  
  Do labels work with busses the same way the do with single wires?
  


No.  There are some bus-specific label requirements (see http://docs.kicad-pcb.org/stable/en/eeschema.html#connections-buses)


  
  Is it correct, that every line from a bus that has the same name, will be connected in the net-list?
  


Wires connected to buses need to have a local label attached to them identifying which bus member they are connecting.  Each bus member needs to have the same alpha-numeric prefix (e.g. ETH1_LED) and a numeric suffix.