Mr. Bean has a house and a good car, but all he does is funny things and nothing else. How does he get paid to buy food, electricity and clothing?
He works. According to Wikipedia in the first film adaptation he has a job as a guard at an art-gallery in London.
“In the first film adaptation, Bean, ‘Mr.’ appears on his passport in the ‘first name’ field, and he is shown employed as a guard at London’s National Gallery.”
We don't know much about his profession and income at the time of where the "Mr. Bean" TV series was recorded (1990-1995).
In the "Bean" film, he has worked as a guard at London's National Gallery (1997). Maybe he already got the job before back in 1990? Maybe.
He promote some well-priced merchandise products like T-shirts and also website creation with Wix.
Not to mention the income from the commercials posts blend in at each video.
That's probably enough to make a nice living in his flat in Highbury.
One of the funny things about Bean is that, as weird as he is, he is at times incredibly competent. For example, in this clip he measures a hole in the wall basically by eyeballing it, and later when he cuts a patch, the patch is precisely correct. It fits perfectly.
So while I don't know exactly what his job is (and I imagine it changes from time to time as he screws things up), it appears he does indeed possess useful skills.
Mr. Bean also had a stint as a politician, once being elected a Member of Parliament for the independent "Bean" party.
A few other sketches hint at other possible jobs - in the first episode, "Mr Bean", he is attending a maths exam, possibly hinting at a need to gain a maths qualification for some reason. In the unaired sketch "The Library" he is copying a page from a rare tome in a library. Of course, these could both be simply other interests of his rather than related to work.