You can use "sed" to manipulate the line. The following expression will pick up anything between "BILL" and "ACCOUNT":
echo "BIP in report_one_acnt> **SUCCESSFUL** BILL 25895519 ACCOUNT 7615" |\
sed 's/^.*BILL //; s/ ACCOUNT.*$//'
The first regexp cuts away everything before and including "BILL " (with a space following), the second cuts everything from " ACCOUNT" (with a leading blank) to the end of line, which leaves solely the number.
Still, this might have to be checked if it is indeed a number (for instance, "...BILL FOOBAR ACCOUNT..." might break whatever follows, because the extracted "FOOBAR" is NOT a number). You can do this by:
# catch the result in a variable
var="$( echo "BIP in report_one_acnt> **SUCCESSFUL** BILL 25895519 ACCOUNT 7615" |\
sed 's/^.*BILL //; s/ ACCOUNT.*$//' \
)
# test if "$var" contains only digits:
if [ -n "$(echo "$var" | sed 's/[0-9]//g)" ] ; then
echo "$var is not a number"
else
echo "$var is a number"
fi