Awk and grep are good for these types of issues.
New:
ls -l /proc/<pid>/cwd | awk '{print ($NF) }' | sed 's#/dbs/##'
Old:
ls -l /proc/<pid>/cwd | awk '{print ($NF) }' | egrep -o '^.+[.0-9]'
Awk prints the last column of the input which is your ls command and then grep grabs the beginning of that string up the last occurrence of numbers and dots. This is a situational solution and perhaps not the best.