HMV, the UK record retailer, has introduced a series of CDs under the title "All Time Greats", and possibly the most deserving of that title is our Bing.
Each title consists of a 2CD set and Bing's has a total of 40 songs.  As might be expected many are those that regularly crop up on every other compilation that comes out, but there are a few are not quite so common and the set is quite an attractive bargain for those in need of the tracks in question, at £4:99. It is "Exclusive" and I don't think you'll find it anywhere other than HMV's own shops and website, nor will they send outside the UK. Orders over £10 are post free, so examination of their other offerings could be called for.  Sound quality is good. There are no notes but writers and accompanists are given. 
Link here - https://store.hmv.com/store/music/cd/all-time-greats-(hmv-exclusive)-(3)

But as HMV seem to be sufficiently lethargic to ignore listing the tracks they are - 

CD1
1 Dear Hearts and Gentle People
2 Around the World
3 Chattanoogie Shoe-Shine Boy
4 Galway Bay
5 Gone Fishin'
6 Count Your Blessings Instead of Sheep (Listed as "Count You Blessings  - -" on the inlay tray)
7 Temptation
8 The Isle of Inisfree
9 Quicksilver
10 Changing Partners
11 Shanghai
12 Stranger In Paradise
13 Mule Train
14 Harbor Lights
15 Play a Simple Melody
16 Far Away Places
17 Whiffenpoof Song
18 Sunshine Cake
19 Some Enchanted Evening
20 White Christmas (listed as "1942 Holiday Inn version")
CD2
1 Pennies From Heaven
2 Don't Fence Me In
3 Moonlight Becomes You
4 Deep In the Heart of Texas
5 How Can You Buy Killarney?
6 You Are My Sunshine
7 If I Had My Way
8 Swinging On a Star
9 Sierra Sue
10 Pistol Packin' Mama
11 Only Forever
12 MacNamara's Band
13 Please
14 San Fernando Valley
15 Sunday, Monday Or Always
16 I'll Be Seeing You
17 On the Atchison, Topeka, and Santa Fe
18 Ciribiribin
19 Too-Ra-Loo-Ra-Loo-Ral
20 In the Cool, Cool, Cool Of the Evening