Bostock, who previously said she was in “awe” of the fast-growing website, admitted that Asos was “not the right place” for her.
Her shock resignation came a year after she announced she was leaving as head of general merchandise at M&S, having spent eight years with the high street stalwart.
Described as one of the most influential women in British fashion, her hiring was seen as a coup for Asos, which was established in 2000.
But the switch to the fast-moving online fashion world did not work out. She said: “Asos is a formidable business and I have great respect for the team I have been working with: they are right at the cutting edge of young online fashion. Sadly, I’ve concluded that Asos isn’t the right place for me.”
Bostock’s departure echoes that of “knicker queen” Janie Schaffer, who quit as director of lingerie and beauty at M&S in April, after just three months in the role. April also saw the resignation of Asos’s international director Jon Kamaluddin, while product director Robert Bready quit in October.
It is not known what Bostock’s next move might be, although analysts suggested the likes of New Look or Sir Philip Green’s Arcadia group may be better suited to her corporate background, which includes spells with George at Asda and Next.
Retail analyst Nick Bubb said: “A lot of people thought it was an odd move to go to Asos, which is by definition faster moving. The sceptics have been proved right.”
Asos said Bostock’s role will be filled by its existing “highly successful” retailing team and the firm’s board was yet to decide whether there was a need to replace her.
Co-founder and chief executive Nick Robertson said: “Kate and I have agreed that Asos is not the right platform for her talent. Of course we are disappointed that things haven’t worked out and Kate leaves with our very best wishes.
“In the meantime, we have a very strong team in place and the business continues to fire on all cylinders.”
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 her share of a bonus pot, worth up to £30 million, which will be divided between 24 top managers if they hit a series of tough sales targets by 2015.
Asos targets young shoppers aiming to emulate the designer looks of celebrities such as Cara Delevingne and Nicole Scherzinger, and last month reported a 45 per cent surge in total retail sales to £194m in the three months to the end of May, helped by strong growth in overseas markets.
The firm has 6.5 million customers and 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”, is targeting sales of £1 billion by 2015.