I rarely had this problem in the morning as mine never slept that late to be honest. But once she was mobile, I made sure there was always some sort of barrier up against the side of the bed (this is mainly for evenings). We used a sidecar cot for this (just because it had always been there), so cot against her side of the bed and then it was unlikely she would get across to the other side of the bed before I could hear she was awake. We did go through phase around 8 months when she first started to crawl and she would literally pop straight out of sleep and start crawling across the bed. She nearly fell off about 3 times before I could run up the stairs to grab her. For a bit, we just started to put her to sleep in her cot in the evenings and would go get her when she first woke up once we were in bed. But in the mornings, it was rare I was too far away, so I wasn't as concerned. Once she was a bit older, past 1, she was much more aware of her surroundings and I could leave her in bed if I needed to and she wouldn't just fall out. Or if it was morning and she woke, she could easily just get down on her own. But a cot or a bed guard up against that side does help in the meantime.
