The minibus is one a day usually though sometimes there are more, it leaves Mfuwe at 1am 'officially' but its more like 3-4am. The trip takes about 5-6 hours so if you are at the bus station in Chipata at 9am you should be able to jump on it and go the other way. If you try and take a cab you will be quoted quite high prices, the best I have ever got one for is $80. There really is just one road from Chipata to Mfuwe, if you can get to the road it should be very easy to hitch, I managed it going the other way as most of the campsites run to Chipata once a week for supplies and such.
You should be able to get a taxi from the border at Machinji to the bus station in Chipata for a few dollars, when you get there look for the blue minibuses and ask for Mfuwe, if there are not any there then you will easily be able to get a cab but remember to negotiate!
The road is very tough though so be prepared for a harsh ride, oh and don't wear anything white!
Oh, one more thing, if you get a minibus it should be able to drop you off at your campsite if you ask (a cab will also do this). If you get dropped off in the town of Mfuwe you can easily hitch to one of the camps in any of the 4x4's on the road, most will be going to one of the camps by the river. It is dangerous to walk it