An interesting question, Roma..... and one which prompted me to make a search, becasue Ian's maternal grandparents lived in Beeston, Leeds, and I wondered if there was any connection. There does not seem to be!
From wikipedia, though, comes this:
Origins of the name Beeston
The earliest recorded name given to the area was Bestune. This is now generally thought to be derived from "bes" = rye grass and "tune" a farmstead settlement. The description of local pasture is still preserved in the name of Beeston Rylands. However there are alternative derivations from "Bedestun" = the farm of Bede or (even less probably) from Saint Bees.
In the late nineteenth century, a genteel convention was contrived that the town's name derived from bee. This would have also been consistent with the notion of Beeston as a "hive of industry". The bee was adopted as the emblem of the town council. Beehives appear carved in the brick of the town hall exterior, and in 1959 three bees were included in the coat of arms adopted by Beeston and Stapleford Urban District Council.
However, as this derivation was known to be dubious, the College of Arms subtly included some long grasses entwined with meadow crocuses in the arms as an alternative visual pun on the more likely origins of the name. With the formation of Broxtowe District (later Borough) Council in 1974, the bees were carried on to its coat of arms, representing Beeston. The tradition of the bee as symbol continues - the litter bins and other street furniture in the High Road are decorated in black and gold, with a symbol of a bee on each.
There is also a sculpture on the High Road of a man sitting next to a bee hive. Again, this is another reference to the "Bee". The sculpture is popularly known as the "Bee-man", "the man of Beeston", "The Beekeeper" or "Bee King"
So it seems the atrractive Bee man and his sculpture are just public relations tricks!