You can use the DateTime class to obtain the current date and time to compare against.
And to get AM/PM you can use the .ToString to format the time object
You will need to determine how many minutes allows for your to round up vs retaining the current hour (e.g. does 8:29 -> 9:00 or does 8:29 -> 8:00?)
After you determine when to round up, you need to get that future day/time and then parse the DateTime properties mentioned above to be able to select the day/time in your drop down boxes.
Remember to create an instance of the DateTime object and use that variable throughout your checks. If you run Now over and over, you may have part of your process thinking it is 11:29 and another part of the process thinking it is 11:30