Make your conditions like this:
IF Cell Value is between [=TODAY()] and [=TODAY()+15]
where [] indicates the boxes where you type the conditions
This is slightly different than the way you worded the question because I am
looking at your A column values instead of B, but since they are just a fixed
number of days apart it just means the condition is somewhat different - I am
looking at is as "am I less than 15 days away from the deadline???" Easier
for me at least to conceptualize and get the formulas right!

"Bob Reynolds" wrote:

Hello, I have a worksheet that cell A1 is calculated with a formula =B1+45
and it is formatted to display as a date. The date entered into cell B1 will
be displayed as 45 days ahead in A1.

I need to conditional format cell A1 to show a yellow background color if
TODAY's date is is equal to or greater than B1 plus 15 days; Yellow
background if TODAY's date is equal to B1 plus 16 days but less than B1 plus
30 days; and a Red background if TODAY's date is greater than B1+31...

I can't get the colors to change since the date in the cell A1 is always 45
days.
Basically cell A1 tells me the 45 day drop dead date and I want the cell
background color to give me visual warnings as to what stage the time is in.

Any ideas how I can make this work???