I graduated with a dual BA in Urban Studies and Historic Preservation. I've been working for a few months in a well-paid (but no benefits) internship. I will start a really great historic preservation planner position in 2 weeks.
If you can secure 1 or 2 good internships as an undergraduate, you can find an entry-level planning position with a bachelor's degree. Like any career, your long-term opportunities for advancement will be greater if you have a graduate degree.
At least with an undergrad degree, you can work for a few years in the planning field, figure out what you want to specialize in, and put some money in savings. That way, when you start your graduate studies you'll have more focus and (hopefully) less debt.