Light-aircraft charters are possible to access Bubaque town from both Bissau and Dakar, Senegal. It's a pricey means of reaching the islands.
It's wise to exercise caution when contemplating taking any kind of boat from Bissau during heavy rains.
Ilha de Bubaque is the gateway to the rest of the Bijagós, with the exception of Ilha de Bolama and a few of the more out-of-the-way private resort islands.
The former ferry Expresso dos Bijagos left Bissau port for Bubaque every Friday, returning from Bubaque on Sunday. Exact departure times depended on the tide but were generally between 9am and 3pm. A replacement was said to be on its way from abroad.
On other days, your choice is between rough and risky canoas (motor canoe; per person CFA2500, six hours) and speedboats (per four-seater boat CFA120,000 to CFA250,000, two hours). You could contact one of the resorts with speedboats (a few on Bubaque and the two on Iha Rubane) in advance and see if they have any space. Or you could head down to the pier in the morning and ask around and see if there happen to be any heading out. On good weather days in the high season, odds are you'll find a spot, if not on the first day, then the following or one after. However, of course, you need to patient and have plenty of time and flexibility.
Or you could pony up for a private plane (from CFA250,000 per person).