Why is the bandwidth doubled with AM? Let's say I have an arbitrary signal which has the following frequency spectrum and a bandwidth of BNF:



Now I use Amplitude Modulation to transport the signal. The frequency spectrum will change accordingly:



Now I know that the required bandwidth doubles. I don't understand where the doubled bandwidth applies as I can't transport negative frequencies.
What you've observed is just the difference between baseband modulation (your original plot) and carrier modulation (the second plot). Note that for the AM case, since the signal that modulates the carrier is real, the resulting carrier-modulated signal is symmetric. This means that you can get away with only transmitting one of the sidebands. This approach is called single sideband (SSB) modulation. With an SSB system, the carrier-modulated signal only has the bandwidth of approximately one of the sidebands of the original baseband signal.