He was eventually spotted in a field about a mile away from home in the Gornal Wood area after being finally traced through the use of social media.
His distraught owner Kate, a 39-year-old children's party entertainer and tutor, said: "We moved house from The Straits in Gornal to Gornal Wood in January and Bob went missing on February 5.
"We have two cats and a dog and the other cat, Cala, is much wiser than Bob.
"Bob is not a friendly cat, only to those people he knows and after the move he did not want to go out.
"I was trying to persuade him to go into the garden and went out with him and only popped into the house to make a cup of tea and to get my phone and he was gone.
"I looked for him and was beside myself when it went dark and he had still not returned.
"Over the weeks I did everything to try to find him and put up posters on lamp posts and a banner as well as making appeals on social media.
"It was my mother, Elizabeth Poulton, from Sedgley, who refused to give up hope of finding him and eventually a woman contacted me on Facebook and said that her friend's mother had seen a cat looking hungry in a field about one mile away in Tansey Green Road, Pensnett.
"I went up there and called his name and shook a packet of biscuits, his favourite treats, and heard him cry.
"I was so excited and videoed the whole thing and now Bob has become a bit of a local cat celebrity.
"It has gone viral and I cannot say how ecstatic I was at finding him and have now placed him on permanent lockdown at the moment with a litter tray in the garage.
"He has been checked over by a vet and although he is looking a bit thin thankfully he is fine.
"When he went missing I had this overwhelming sense of responsibility that it was my fault but he was just not ready to go out.
"I think it shows people should not give up hope and continue searching when a pet goes missing and that the use of Facebook can be an invaluable tool."