You got the result you wanted. The BB called with an inferior hand and made a mistake. You just got unlucky - so 50p please.
The way the hand played out, the flat call or the shove pre-flop would have produced the same result.
I doubt that the BB calls a shove pre. Not for all his chips.
By flatting we give him decent odds to call with hands exactly like the one he had and then make his mistake on the flop.
Played perfectly, just unlucky.
WD on the 3rd