How to increment a date in a Bash script

startdate=$(date -d"$1" +%s)
next=86400 # 86400 is one day

for (( i=startdate; i < startdate + 8*next; i+=next )); do
     date -d"@$i" +%d-%m-%Y
done

Use the date command's ability to add days to existing dates.

The following:

DATE=2013-05-25

for i in {0..8}
do
   NEXT_DATE=$(date +%m-%d-%Y -d "$DATE + $i day")
   echo "$NEXT_DATE"
done

produces:

05-25-2013
05-26-2013
05-27-2013
05-28-2013
05-29-2013
05-30-2013
05-31-2013
06-01-2013
06-02-2013

Note, this works well in your case but other date formats such as yyyymmdd may need to include "UTC" in the date string (e.g., date -ud "20130515 UTC + 1 day").