"a formula that looks at both of these fields and returns a conditional warning that the date field has no date in it." - what's the condition of the second field that it has to evaluate?
If you mean that the condition is for example that there is a Bill-to name, and yet there is no date, then you could format it to highlight under these conditions:
BillToName ≠ "" and DateField = ""
The second field condition is a specific bill to name, since the bill to names can change there is only one bill to name that this applies to, so if the bill to name is "XYZ" but eh date field is not filled in the the conditional warning should execute.