|>>|| No. 2595
You'll want a mole wrench, or if it's too big even for that, a chain wrench.
If you can find it, there's a drain cleaner called One Shot which is 90% sulphuric acid. I wouldn't be surprised if it's been taken off the market in certain places, what with all the acid attacks - if you get this on your skin you will be seriously hurt. It will likely get rid of your bathroom blockage, but you need to be very sure that your drains are PVC/ABS plastic as it will eat metal. Don't get any of it outside the sink as it'll rip the surface off ceramics as well as metal. Don't go plunging directly afterwards or you risk getting a melted face.
Even with that stuff, you'll likely find exactly the problem you've described: after a month the blockage will come back. The fact of the matter is that nothing in a bottle will ever compare to a professional drain cleaner with a rooter. Don't go with your regular plumber, go with the specialists.