Climbing alone a 4000 m. in the Alps? I did it only one time. The only peak that I climbed alone in the Alps was Gran Paradiso, and it was easy: no crevasses and only a short (but dangerous) rocky ridge to get to the summit. But I wouldn't repeat this climb or others with glaciers alone.
Bishorn is a very easy climb to, but you have to cross glaciers in all (I supose) 4000 m. peaks in the Alps, and you don't know if there are crevasses under the snow...
You can find a partner easily if you visit Chamonix or Zermatt. There are lots of people looking for partners to climb; look for in the tourist information of those villages.