I would say gurney instead of stretcher. I imagine it is the sort of bed used in medical environments, so gurney would work, especially for the US.

Wikipedia;
"A stretcher, litter, or pram is an apparatus used for moving patients who require medical care. A basic type (cot or litter) must be carried by two or more people. A wheeled stretcher (known as a gurney, trolley, bed or cart) is often equipped with variable height frames, wheels, tracks, or skids."

Just another option. Definitely gurney, as Marie Wilson said. "Semi-reclined" sounds a little clinical, like maybe from a medical report. "Partially" just seems like a more ordinary, I don't know, *daily* kind of word. So it depends on just what kind of tone you're trying to establish with the vocabulary. Is the narrator trying to present a clinical picture, or more of a personal experience?

Wit that in mind, you might also want to consider something like "partially raised," since the normal position is flat, completely reclined. Using "raised" instead of "reclined" (*I* think) would be a stronger indication of the position's difference from the norm (fully reclined).