You can use the BIOS.Teletype function 0Eh for this.
It's a function that writes the character from AL
to the display page from BH
using the color from BL
. The function also interprets some control codes: 13 for carriage return, 10 for linefeed, 8 for backspace, and 7 for bell. The function returns nothing.
Because sounding the beeper is an audible operation, you can shave off a few bytes and not mention anything for the displaypage or the color.
In the limited space of your bootsector, next is all it takes to beep:
mov ax, 0E07h ; BIOS.Teletype BELL
int 10h