The IDE doesn't seem to have a menu to choose the bootloader. What am I missing?
how do I burn a sketch so that it starts directly without a bootloader?
This is controlled by a series of microcontroller switches (fuses). To change these, you need an external programmer.
If you read yourself warm and fuzzy on "improved" bootloaders, you may want to know that many (if not all) of these improvements relate to ancient versions of the Arduino bootloader.
Doesn't ArduinoISP count as an external programmer?
No. An external programmer is a piece of hardware that typically connects to the six pins labeled ICSP.