I think almost all singers when they start out are strongly influenced by earlier vocalists they've studied.  Various factors, however, determine how close they sound like their mentors.  For example,  pitch range may be different.  (My brother tried to sound like Elvis with a vocal range about a fifth lower.)  The musculature and shape of the mouth and throat may be at variance.  Physical differences also affect the tongue, teeth and soft palate.
For a singer to sound very like another singer, physical similarities are present after which style is applied. Even then he may not have a talent for mimicry.   Michael Holliday had a very fine voice in its own right and was able to make it sound like a 'stylised' version of Bing's with relative ease.  Similarly, Dick Todd was able to replicate the more strident tone and husky power of Bing's early recordings.   But ultimately such gifted singers are at a disadvantage.  It's harder for them to develop a trademark style separate from their idol's.  (Though Perry Como eventually achieved this, as did Dean Martin.)
On the other hand, a singer who has no physical similarities to another and no propensity for mimicry, the path is easier if the essential voice and musicality is up to standard.  No matter how much they aim to sound like their heroes, they can't!  Bing's early efforts owed a lot to Al Jolson, but I never heard Bing do an actual impression of his hero. 
Did he want to?  Would he have known how to?

It's great that so much of Bing's earlier work is finally available without our having to put up too much with technical limitations.  He certainly had a fine unique voice.  My personal preference is for his late thirties work when he started to sound less strident.

A lot of people said when Martin and Lewis split up that Dean, having become famous on the back of Jerry's clowning, would get left behind.  How wrong they were!  However, Dean Martin, for all his success, is probably underrated as a vocalist.  In my view he was the only singer who could match Bing's timing on a laid-back up-tempo number.  His version of 'In The Cool, Cool, Cool Of The Evening' is a brilliant example of 'the art that conceals.....' (see bottom of posting).

The last paragraph of the quotation from Mary Crosby carries the key to Bing longevity as a performer.  He was impressively versatile in his ability to engage with such a wide range of material.  I do find it sad when jazz enthusiasts don't take him seriously because he could also do comedy, or if people who like show music are put off when he's singing a jazz number.  Some of us unfortunately do like to put our vocalists into rigid categories, and modern singers particularly suffer if they can't be pigeon-holed.

I forgot to suggest that Bing supporters who hate Frank, and vice versa, are probably a left over from the days when the publicity gurus wanted to believe that Bing and Frank were feuding.  It wasn't true!  On the contrary there appeared to be huge mutual respect throughout their carrers.

The 'dre - e - aming' was what, I believe, Gary Giddins meant when he wrote of Bing's use of the 'mordent', something Bing apparently borrowed from the old Irish tenors he was so fond of.  It was extensively copied by the crooners who most closely followed Bing in the 1950s (e.g. Dean Martin; Perry Como), though Bing used it less and less as his career progressed.  He'd probably already begun to tire of it when he recorded the second version of 'White Christmas' in 1947.

I'm delighted to see the launch of such an apparently well organised site in the cause of preserving Bing's legacy.  As an occasional contributor to Steven Lewis's 'Internet Museum', I was sad to see its demise.  I hope your site goes from strength to strength and serves to complement the increasingly impressive official Bing Crosby site.
All the very best.
John Walton