If I use USBtinyISP to burn the bootloader from the IDE, does it select the .hex file to use based on the IDE:Board setting
Yes. If you'd like the details, the mapping from menu selection to .hex file is in a file named "boards.txt".
or is there an additional dialog where you set that?
No.
From your comments, I presume it takes care of all the fiddly-bits as well?
It always has for me. Which is why I use the IDE (brain ... overloading ... on ... fiddly-bits !!!).