If you are just collecting the time of day, such am or pm, I would keep it separate from the date column.
I would only combine the two if you were considering a full date/time stamp such as "2009-10-18 22:00:00".
But since the exact time is not what you are looking for, I would go to two separate columns.
As far as searching both, why couldn't you search by both attributes. It would be real simple, actually.
In your search form, you would just run validation to ensure that a time of day was selected (which would happen automatically if you used a drop down menu for the time of day column).
So, I would have your date field be text in the search and then add a drop down menu for time of day that only included "am" or "pm" with the appropriate values and then add validation to the form to ensure that am or pm was selected and then search away.