What is a reasonable relocation bonus for an individual moving from PA to DC?

Depends on how badly the company wants the person and what the salary range is for that position. My standard has been 10K (grossed up) and housing for 3 months. But that's just what it takes to get me to move. Your case may be different.

Most companies don't give any now adays, others will pay only actual expensies, normally your company will have a standard set amount for such moved