Does a bedridden patient have to have someone there 24/7?

If this person is competent mentally, if there are alarms installed in the home in larger than normal numbers, including carbon monoxide alarms, if emergency response in your neighborhood/town for 911 calls, if someone is aware that this person is alone, and is responsible to receive calls, then the answer is that 24/7 person is not needed. However this doesn't mean OK to be in home daily this way, but for several hours at a time. This would be my opinion and my "guess".
Just this Christmas we had an incident. Have a two flat in which we live above our tenants. Their stove did not go on; something about the flame starter. Carbon Monoxide alarm went off. Count this under something can always happen that needs addressing, in a moment. It doesn't happen often, but it CAN happen.

I don’t know if I would be comfortable doing it all the time. However, some days it just can’t be helped. Like the other day, we all had something to do in our town that probably took a couple of hours not 24/7 like you are asking. We got dad in his recliner and let him know we had to be gone for a while (I use we're going to get him something good to eat. He loves to eat). I also let everyone know that if I saw him get out of the chair, whoever was close would have to drop what they were doing and get back to him. Thankfully he stayed in his chair until we got back. Unfortunately, respite has not been working out to give us relief not even when notice is given well in advance and we just have to go. 

What gladimhere mentioned are valid concerns but that can also happen at a nursing home, assisted living, or any other facility where they are fully staffed or maybe not fully staffed that day. I guess you have to ask yourself, could you live with that or could you get in trouble if something like this were to happen? I imagine most of us are doing the best we can.

You probably would need someone to keep stopping in to, at the least, make sure she gets to the potty (bedsores/wound) and has done other things that will need to be done in that 24/7 time (meds you mentioned). I would probably want home monitoring other than just me trying to watch from my phone both inside and outside of the home. Do you have anyone you can really count on other than yourself if there is ever a time you can’t be the one to make the stop?

[Patient has a hard time occupying time.] Not sure what you meant with that statement except maybe for example tv will only satisfy temporarily. You also did not state why the bedridden patient needs to be left 24/7 (work for example or trying to keep them in their own home and you in yours) so kind of guessing and hoping something helps you come up with a clear plain of action.

Realistically, if you can't have or can't afford someone there 24/7, then you can't.

The last 3 months, both of my mom's sitters were out on medical leave. Both had surgery, one very serious and complicated surgery which put her out of commision for 6 months at least.

I had to make do with what I had. No choice. Abandoning my kids and husband to stay with my mom 24/7 is not an option. So, my mother sometimes sleeps by herself overnight when my aunt goes out with her friends. My mom doesn't get out of bed until I come in the morning and get her out. During the day when she naps, she can be left alone if needed.

What if there were a fire, natural gas leak, anything where she needed to get out of the house?