It’s in the database, but it’s encrypted (the type of encryption depends on which version of bbPress you’re using.) So, you can retrieve the encrypted value with something like phpMyAdmin. Once you have the encrypted value, you can’t just decrypt it. The encryption is one-way. You can use something like rainbow tables to crack the password hash, but that’s beyond the scope of this discussion I think.
I think there is probably an easier way to accomplish what you want to do without dealing with the encrypted password. What is it you want to do exactly?
In all honesty, you will not find a solution with less steps and ease than requesting a new password, checking your email, logging in and then changing password in the profile edit screen. Even a “copy and paste” of your current hash from the database would take more screwing around.