In Bissau minibuses called toca-toca provide transport within the city. There are also regular taxis. For inter-city travel there are sept-places, seven-seat Peugeot and candongas, big commercial vehicles carrying ten to twenty passengers. Prefer sept-place or at least try to get the front seats. It is also possible to rent taxis to other towns and cities.
The main bus-station "paragem" of Bissau is situated behind the BCEAO Banco Central dos Estados de África Ocidental on the Airport Road. Are you heading for Biombo or Prabis, you need to go to another bus-station in Estrada de Bor. There are no time-schedules; cars leave when they are full. As most locals travel in the early morning c. 07.00, cars fill up quicker in the morning. It might be hard to get transport in late afternoon and evening.
To go to the islands, there's a choice between cheap, but rather unsafe, canoas pirogues leaving from Porto Pidjiguiti or Porto de Bandim, and expensive modern boats owned by french fishing lodges on the Bijagos islands. In 2007 a ferry started sailing between Bissau and Bubaque, leaving Friday and returning Sunday. Schedules depend on tides, so check in advance.
As Guinea Bissau is very flat and there is virtually no traffic on the roads outside Bissau, it's a good country for cycling. Bikes can be bought in the country, which will probably as in most parts of the world be Chinese made bikes. As always, good value for money.