Asos recently delivered its best UK sales growth in four years, but chief executive Nick Robertson said the appointment of Ms Bostock, who joined in January as executive director for product and trading, had not worked out.
Ms Bostock, who was reported to have taken a cut from her £944,000 pay package at M&S when she joined Asos, will receive no severance deal from the online retailer because she has resigned.
The move also means she will miss out on the lucrative share bonus pot worth up to £30 million that will be awarded to 24 top managers if they hit a series of tough sales targets by 2015.
Ms Bostock said at the time her appointment was announced last October that she was "very excited" about joining the company, but her enthusiasm turned out to be short lived. Announcing her immediate departure, she said: "Sadly, I've concluded that Asos isn't the right place for me."
Asos said her role would be filled by the existing retailing team and the board would "consider whether there is a need to seek a replacement for Kate".
Ms Bostock's resignation comes a year after she announced her departure from M&S where she was head of general merchandise. She was seen by some as a scapegoat following a dire sales performance fuelled by poor take-up of the high street stalwart's womenswear collection. She has previously held senior roles at George at Asda and Next.
Last month, Asos showed that it was going from strength to strength as revenues surged by 39% in its third quarter, the strongest performance since the third quarter of 2009. It followed efforts to refocus marketing on its core twenty-something customer base and cut price tags as well as offering free delivery and returns.
The firm has 6.5 million customers. It recently announced a tie-up with Primark, allowing the budget fashion chain to sell clothes on the internet for the first time. Asos, which stands for "As Seen on Screen", was founded in 2000 and targets fashion-conscious young people by aiming to emulate the styles of their favourite celebrities. It is targeting £1 billion sales by 2015.