I am developing an app and I know my database *.db
will appear in data/data/com.****.***
I can access this file from AVD in Eclipse with he
You could also try fetching the db using root explorer app. And if that does not work then you can try this:
adb shell
'su
chmod 777 /data /data/data /data/data/com.application.package /data/data/com.application.package/*
After this you should be able to browse the files on the rooted device.