SCP - "not a directory" - What am I doing wrong?

Since you want to copy the file with the same name, you don't need to specify a target name:

scp ~/path/bla/ble/.bash_profile [email protected]:/home/bleble/

Because a .bash_profile exists in the target directory, scp thinks you are giving it a directory as a target, attempts to descend into to it and exits since it is not actually a directory.