Here is the point there is a secured WiFi connection - which password I don't know - but there is an device - Galaxy Nexus smartphone which is already connected to that WiFi and my Galaxy Tab tablet. There is any change to set GN as Bluetooth modem, to tether WiFi connection, for Galaxy Tab?
Android 4.0+ officially supports bluetooth tethering in both directions (and allows bridging to whatever the internet connection is (wifi/usb/3G)).
You then can connect to the tethering profile:
The GNexus fulfills all of that, however your P1000 cannot officially upgraded to Android 4.0 though, so you're out of luck or you have to install an aftermarket firmware (e.g. CyanogenMod9, which is based on Android 4.0.4)