Problem:

For some species the Darwin's theory evolution makes perfect sense. I can easily imagine how, for example, the giraffe has evolved to its current appearance: the natural selection was favoring individuals that could consume more vegetable food from trees using longer necks, and some individuals were getting at birth necks longer than average by pure genetic randomness and the long neck trait was being propagated to descendant individuals by means of genetic inheritance. I have no problem with understanding this kind of evolution.
Now let's have a look at the bat and its relatives. The bat is one of the few mammals that have something to do with flying and the only one that took flying to the bird level. Paleontologically, first mammals date to the dinosaur era and initially looked similar to the present-day shrew (which looks much like a mouse). The question is: how in the world prehistoric mouse-like creatures could grow wings over time? It impossible to believe that some mouse-like individuals were getting wing-like limbs by mutation and the "wings" were growing out accompanied with the knowledge of how the "wings" can actually be used. Ok, then maybe first wings were tiny moth-size wings and then grew larger? But where natural selection would come into play in this case? Such mouse-like individuals would have no advantage over their wingless relatives and thus would not be able to transfer those wing-growing genes to their descendants, quite the contrary, such individuals with useless mutations that interfere with their ability to walk would be suppressed by natural selection and therefore "weeded out".

Question: What is the story behind the bat's wings and is the Darwin's theory really able to support it? Please justify your answers.