Game is designed to work with a single button joystick.
You can only take out a bomb or throw a rope when not carrying another item.
To take out or put back a bomb, hold button for a second while joystick is centered. Note that at this moment the bomb is not armed yet, so you can walk around freely while carrying it. Only after a short button tap, the bomb will be armed. Now you have a few seconds to drop it (joystick down and button tap) or throw it away (button tap). You can only put a bomb back when it's not armed...
It takes some practice to master this :)