Let me see if I understand what you're trying to do.
1) You have a non-smartphone (feature phone) that has data capability for things such as its mini-browser, and also can provide an Internet connection via Bluetooth.
2) You want to use the Internet connection on the feature phone to connect your tablet to the Internet, i.e. your tablet does NOT have a cellular internet connection of its own.
3) Your logic is that the feature phone can provide an Internet connection via Bluetooth to a laptop computer; therefore, it may be possible to do the same to an Android device.
What you're asking to do is in theory possible, but from my own research does not appear to be possible without rooting the Android device, and even then is only possible for wired, not Bluetooth, devices.
Here's why: To connect to the Internet over Bluetooth from, say, your laptop, there's two possible protocols. One is using the Bluetooth Serial Port protocol, which basically causes your phone to emulate an old-fashioned modem, and two is the Bluetooth Personal Area Networking protocol, which causes the Bluetooth device to behave like a network card. Since you've indicated "dialing" numbers (e.g. *99#) it is clear that your feature phone uses the modem protocol.
So what's basically happening is that your Feature phone, which has an Internet connection, is "pretending", over Bluetooth, to be a traditional telephone line based modem. Your laptop is "dialing" that modem, which instructs the phone to make an Internet connection and offer it over this virtual modem.
The protocol used to provide Internet connectivity over serial links is called PPP (Point to Point Protocol). Back when most people dialed into the Internet over the phone, it's what almost everyone used to get online. Today, it survives largely in the form you're referring to - as a way to push an Internet connection from a relatively cheap, less powerful phone to a more powerful computer. (It's also used for VPN's, but I digress.)
Here's the problem. Android, since it's designed to be the device with the Internet connection (and it would usually be the one to share it, as well) does not come with native support for "dialing" an "external modem". Android is based on Linux, and as an operating system Linux certainly can support this - it used to be used this way all the time. However, modern versions of Linux have tended to omit features that have little or no practical application today.
The only tool I did find online that can enable PPP and dial-up support on an Android device is called PPP Widget, located here: http://www.draisberghof.de/android/pppwidget.html
This tool won't meet your requirements, however. One, it requires rooting the device, and two, it's for USB modems, not for Bluetooth "modems". This doesn't mean it's not usable for your purpose, because a lot of feature phones that provide Bluetooth modems also can provide a "modem"-like interface via the USB port. This will depend completely on the make and model of your phone.
I have not been able to find any further information to indicate that it's possible to enable PPP and dial-up support without rooting. This is because providing an Internet connection on a Linux device usually requires root access at some level, since the network software has to be reconfigured to work with the new connection and this requires root access.
In theory, someone could write and publish an app to the Play Store that supported exactly what you wanted (Bluetooth modem support with PPP), but given the low demand I sadly don't think it's going to happen.
I hope I've at least enlightened you a bit, and if you need more info reply and I'll help if I can.