There are at least two ways to do it:
Following example performs string replacement using sed.
# sed removes leading zeroes from stdin
new=$(echo $old | sed 's/^0*//')
bash built-in string manipulation
Following example uses bash buil-in string manipulation with extglob. The extglob is used to expand word '+(0)'. Please verify that your bash is using extglob by running 'shopt' command.
# Removes 1 or more longest occurrences from
# the beginning of the string
Check TLDP for more details on string manipulation.