We started BF while lying in bed while we were still in the hospital.
One of the nurses showed us how to do it (they taught us some other techniques too and helped us when we had difficulties (milk threatened to dry up again and kid not wanting to latch on and screaming at the breast instead).
I often read while the kid's nursing and sometimes we both fall asleep that way.
How we do it: I just roll onto my side, stretch the bottom arm out above my daughters head, she's lying on her side too, flat on the mattress and I see to it that her mouth is level with the nippel.
I sleep on my side, so lying on my side is a position I'm comfortable in and which is stable for me (knees are bent for stability; bottom arm spread out, either straight or slightly bent).
For changing sides, we roll to the other side. (She used to sleep on a big towel in bed, so I could pull her (or rather the towel with her on top) close without lifting and then, after nursing, pull her back into the baby balcony attached to our bedside, also without lifting. These days, I just hold her close to me and well roll over together. She's so adept at latching on by now (2 years old) that she will latch on to the other nipple while I'm still in mid-turn.
I'll keep my fingers crossed that you can get BF while lying down to work for you!