Swag lamps are designed for this (plug into the wall, cord runs up and drapes to a hook that supports the fixture). Any reason you aren't considering that?

You could also run surface-mounted wiring (aka electrical raceway). You can paint it the wall color.

Or you could get by with floor and table lamps. You can get lamps that throw light upward to bounce of the ceiling for ambient light.

Battery-operated lighting sounds like it would be annoying. Even with low-wattage lighting, the battery is going to die more often than you will want to climb a ladder to replace it.

Since this is a bedroom, why won't lamps do? Every bedroom in my house is without an overhead light. You just have to get some decent lamps on some furniture, bedside tables, top of a dresser and maybe a nice floor lamp for when you need even more light. Don't go with undersized lamps from places like target, but full size lamps.

You don't need lights on the ceiling to have a well it room.

If you don’t want to hang the lamps permanently from the ceiling, you could go higher on a wall with a pendant light using a bracket to hold the light in place, and plugging into the outlet. If you’re looking for lighting for a specific purpose, such as a closet, there are battery-operated motion lights but one-used twice a day, for not too long, has only lasted me a few months and will need new batteries soon.

Guys - thanks for the ideas. The light we have now isn't great, and I've always had ceiling lights in my other houses. I like the idea of the pendant lights, actually, on either side of the bed, but we'll see.

I had never really thought of those or swag lights, both of which might work well.