How to get time in HHMM format few minutes hence the time now

With GNU date you can do it as simple as this:

date --date="3min"

But busybox seems not so smart (yet). The only reliable solution I came up with using bb is:

busybox date -D '%s' -d "$(( `busybox date +%s`+3*60 ))"

(you don't need the busybox parts if there is no other date implementation present)

If you want a formatted output, you could add this

busybox date -D '%s' +"%y%m%d%H%" -d "$(( `busybox date +%s`+3*60 ))"

if the user is allowed to use at command, this is the perfect use for that:

$ at 08:00 022116
at> myscript.sh
at>      <----------- ctrl-d here
job 9 at 2016-02-21 08:00

if you get a message like "user blah is not able to run at", ask the syadmin to add this user to at.allow file or remove from at.deny file, depending on how it is used in your environment.

Unless of course you wish this days long sleep happen in the middle of your script. Even then you can cut up your script into two, writing variables you want to keep, to a file and when the time comes and second part of your script executes, it can read those variables from the stored file.