How to convert Excel values into buckets?

A nice way to create buckets is the LOOKUP() function.

In this example contains cell A1 is a count of days. The vthe second parameter is a list of values. The third parameter is the list of bucket names.

=LOOKUP(A1,{0,7,14,31,90,180,360},{"0-6","7-13","14-30","31-89","90-179","180-359",">360"})

The right tool for that is to create a range with your limits and the corresponding names. You can then use the vlookup() function, with the 4th parameter set to Trueto create a range lookup.

Note: my PC uses ; as separator, yours might use ,.
Adjust formula according to your regional settings.

May be not quite what you were looking for but how about using conditional formatting functionality of Excel

EDIT: As an alternate you could create a vba function that acts as a formula that will do the calulation for you. something like

Function getBucket(rng As Range) As String
    Dim strReturn As String

    Select Case rng.Value
        Case 0 to 10
            strReturn = "Small"
        Case 11 To 20
             strReturn = "Medium"
        Case 21 To 30
             strReturn = "Large"
        Case 31 To 40
             strReturn = "Huge"
        Case Else
             strReturn = "OMG!!!"
    End Select
    getBucket = strReturn
End Function

Another method to create this would be using the if conditionals...meaning you would reference a cell that has a value and depending on that value it will give you the bucket such as small.

For example, =if(b2>30,"large",if(b2>20,"medium",if(b2>=10,"small",if(b2<10,"tiny",""))))

So if cell b2 had a value of 12, then it will return the word small.

Hope this was what you're looking for.