The B+ wire is likely alright if you noticed it on time, but the problem is due to the drained battery and the bad connection around the fuse. If it was the wrong gauge or something, it wouldn't melt around the fuse but likely elsewhere or wouldn't provide enough current to cause any damage.
This happened to me on 2002 Beetle a week ago. After my alternator died, I, apparently, drove on battery till it died in turn and I had to be towed. Alternators are meant to maintain battery charge and not to charge a totally dead battery as it would draw a very high current that may damage the alternator and, yes, melt the fuse. I replaced the fuse box, sanded well all the contacts, replaced 110A fuse, and greased everything up while charging the removed battery by a dedicated battery charger. The ammeter on the charger was showing very high current for a first couple of hours.
While replacing $150 worth harness won't hurt, get a peace of mind and buy a battery charger to use next time alternator dies.