A more radical and interesting thing you can do is get a set of rollers and ride them. I've been riding resistance rollers for about 25 years. Rollers are a bit hard to get used to, but starting riding in a doorway will increase beginning confidence. It's just like riding on the road - one steers with weight shift, not the bars. I use rollers with a resistance unit so I can do intervals, etc., on them. Rollers are real simple - just put your road bike on them and ride, no fussing around and you're riding the same bike you'll use outdoors. 79 and can still ride the white line if I work at it. It always amazes me to follow fresh bike tracks on pavement and see how much most riders wobble.

It's hard for all those who ride single bikes to get started on a hill. That's a wonderful thing about tandems: Stoker gets the bike rolling.