Subtracting two timestamps in bash script

If you need to use bash, you need to convert the timestamp into an integer value:

$ time="12:34:56.789"
$ IFS=":." read -r h m s ms <<<"$time"
$ echo $h $m $s $ms
12 34 56 789
$ milliseconds=$(( (h*3600 + m*60 + s)*1000 + ms ))
$ echo $milliseconds
45296789

Then you can subtract to get a number of milliseconds representing the diff.

Convert to seconds with some arithmetic and string construction:

$ seconds="$((milliseconds / 1000)).$((milliseconds % 1000))"
$ echo $seconds
45296.789

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To address gniourf_gniourf's valid point (in a clunky way):

$ time="12:34:56.7"
$ IFS=":." read -r h m s ms <<<"$time"
$ ms="${ms}000"; ms=${ms:0:3}
$ echo $h $m $s $ms
12 34 56 700
# .......^^^

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Also, strings that are invalid octal numbers like "08" and "09" will throw errors in bash arithmetic, so explicitly declare they are base 10

milliseconds=$(( (10#$h*3600 + 10#$m*60 + 10#$s)*1000 + 10#$ms ))

If you want to process the date using simple command line tools, you need to convert the timestamps into some easy-to-deal-with format, like epoch-based.

You can do this with the date command, which you can wrap in a function like so:

timestamp() { 
    date '+%s%N' --date="$1"
}
# timestamp '2020-01-01 12:20:45.12345' => 1577899245123450000

Then you can subtract them directly:

echo $(( $(timestamp "$etime") - $(timestamp "$stime") ))

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Note that the %N format specifier (nanoseconds) is a GNU extension and is not handled in the default macOS date command. Either (a) brew install coreutils and use gdate in the function above or (b) use this alternative function on macOS (but note it lacks support for sub-second measurements):

timestamp() {
    local format='%Y-%m-%d %H:%M:%S'     # set to whatever format is used
    date -j -f "$format" "$1" '+%s'
}
# timestamp '2020-01-01 12:20:45' => 1577899245