As ABV says, when the lifts in the Greenwich tunnel aren't working, the stairs are a nightmare (probably worse for you as the bulk of cyclists will be travelling in the opposite direction and there isn't room for 2 bikes to pass except at the slightly wider parts at the landings). When the lifts are in action, it's fine.
The ferry usually runs as a pair. I'm not sure of the operation times but, as it carries a lot of freight, it probably starts pretty early on weekday mornings and will operate until at least 8pm.
Ooh look, a timetable:
Woolwich ferry
The Woolwich ferry is a free service operating between Woolwich and North Woolwich, linking the north and south circular roads across the Thames.
Normal ferry schedule
The ferry service operates every 5 to 10 minutes. Here is the normal ferry schedule:
Monday to Friday
- 6.10am to 8pm (two-boat service)
- Last boat from South to North 7.45pm
Saturday and public holidays
- 6.10am to 8pm (one-boat service)
- Last boat from South to North 7.45pm
Sunday
- 11.30am to 7.30pm, one boat (15-minute service)
- Last trip South - North 7.15pm