It's safe to assume Apple executives look at Bing and estimate the costs and potential ROI when considering their own plans for an in-house search engine.
Also they don't have to spend it all at once, they have been crawling the web for a long time already and are not starting from scratch. So far it's just more in the background and integrated into the OS (Siri etc.)
That ~$11 billion is revenue not profit. We'd have to compare Bing's lower profit numbers to the various reports ($4-$7 billion? $18 billion?) of Apple payments from Google.
Microsoft doesn't break out profit/loss for Bing in its financial reports so we (as outsiders) can't calculate an ROI. It's probable that Apple has enough inside info from Microsoft to determine if the ROI makes sense for them.
Just to provide some ballpark numbers...
Supposedly, Microsoft spent $100 billion on Bing and the CEO Nadella said the most common search query on Bing is "Google".
https://www.google.com/search?q=microsoft+spent+%24100+billi...
It's safe to assume Apple executives look at Bing and estimate the costs and potential ROI when considering their own plans for an in-house search engine.