Yes, but that "bedridden" child is not going to be kept in bed waiting for the MD to visit. They'll be taken to a clinic or the emergency room, and the MD will examine them THERE -- after they have sat in a crowded waiting room for an hour or so, like usual.
A patient won't be known to have smallpox until an MD has examined them and diagnosed them as having smallpox. And in this day and age, that isn't going to happen in their bed at home, but in an examining room, after the patient has passed through a waiting room.
And of course, a single parent who is working and trying to support a family may not exactly be the perfect "Dr. Mom" when it comes to practicing proper isolation procedures, getting the patient to medical attention promptly, and making sure that they don't wear infected clothes to work, etc.
If there is a smallpox epidemic, there will be provisions made for isolating people in the hospital. You simply don't let contagious people sit around the general population. In the initial stages of the diesase, only a few days, there will be a chance for some infections like that, but once the first diagnosis of smallpox is made, quarantines can start.