Types of work experience and how to get it?

[American_Psycho11]

These programs all want applicants who have work experience but: 

1) What kinds of work experience are they looking for? I was in the Army before my undergrad, so there's 4 years, but places say they want "post-graduation" work experience. I like to believe they won't dismiss that just because it's what I did before undergrad. I worked as a line cook at a restaurant part-time in undergrad but obviously that isn't what they're looking for. 

2) How do you get administrative experience (for an MPA) in just a few years out of undergrad with just a bachelors? This is what we're going to grad school for, why are they looking for it already from a bachelors? 

My biggest issue is that I will be graduating with an English degree. I was dead set on law school for most of my undergrad so I chose English as a good pre-law choice, but the more research I did, the more I realized I definitely did NOT want to go to law school and that public administration and policy was what I was actually interested in. It's not something I'm super happy about, but by the time I realized law school wasn't for me I was too late in the game to change my major, so English it is. I'm worried about trying to gain work experience in something related to the public sector with an English degree and feel like I should just apply to an MPA program with what I've got, meaning 4 years enlisted army pre-bachelors. I did a two year humanitarian church mission in Asia before that so I've got that as well, but any sort of admin or policy experience is nil.