A bus leaves Town A on Saturday night and is supposed to arrive at Town B at 08:17 am on Sunday morning. If the estimated journey time is 10 hours 43 minute, at what time on Saturday should the bus leave Town A?

let's consider midnight as time zero

10:43 - 8:17 = 2:26
So it must have left 2 hours and 26 minutes before midnight, or
the bus left town A at 9:34 pm

or:
we could use international time format
let's add 24 hours to 8:17 to get 32:17

and 32:17 - 10:43 = 21:34
which is 9:34 pm, using the "am pm" notation.

Most scientific calculators will have a button labeled D°M'S
This can be used in the calculation of angles in degrees, minutes and seconds of angle.
Since time has the same ratio of hours: minutes: seconds it can also be used for calculations of time (addition and subtraction only, it makes no sense to multiply two times)

to do 32:17 - 10:43 , enter
32
D°M'S
17
-
10
D°M'S
43
=
to get 21°34'00.00 , which is 21:34 or 9:34 pm