You could use date
command to achieve this. man date
will provide you with more details. A bash script could be something on these lines (seems to work fine on Ubuntu 10.04 bash 4.1.5):
#!/bin/bash
# Date 1
dt1="2011-11-11 11:11:11"
# Compute the seconds since epoch for date 1
t1=$(date --date="$dt1" +%s)
# Date 2 : Current date
dt2=$(date +%Y-%m-%d\ %H:%M:%S)
# Compute the seconds since epoch for date 2
t2=$(date --date="$dt2" +%s)
# Compute the difference in dates in seconds
let "tDiff=$t2-$t1"
# Compute the approximate hour difference
let "hDiff=$tDiff/3600"
echo "Approx hour diff b/w $dt1 & $dt2 = $hDiff"
Hope this helps!