Assuming this is how you get the current time in Joda time:
DateTime now = new DateTime();
How do you calculate values for the variables
This works better, it turns out DateTime has a method called toInterval which does this exact thing (figures out midnight to midnight). In my tests, it appears to have no problem with DST transitions.
DateTime now = new DateTime();
DateTime startOfToday = now.toDateMidnight().toInterval().getStart();
DateTime endOfToday = now.toDateMidnight().toInterval().getEnd();
System.out.println( "\n" + now + "\n" + startOfToday + "\n" + endOfToday + "\n" );
JODA looks to be very well thought out.