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There are definitely more buses than that (not a lot more, but still), at least in the summer when there are a lot of tourists around, but information is difficult to find on the Internet. There are many different companies and they don't all have up-to-date schedules on their website.
The site Corsica Bus seeks to gather information about public transport in Corsica and has information in both English and French. I recommend reading their βCorsica without a carβ page.
From Calvi to Bastia, they list two buses a day in the summer (late June to early September), taking a little over 2 hours. In the winter there's only a single weekday bus. Alternatively there is a train, taking a little over 3 hours, with 2 connections a day at different times in summer and winter.
From Bonifacio to Calvi, it's not so good. The only suggestion is a combination of three buses, the last one being the Bastia to Calvi bus β Bonifacio-Bastia-Calvi would be easier than Bonifacio-Calvi-Bastia. You'd take the early morning or midday bus from Bonifacio to Porto Vecchio (do check because that company haven't announced their July schedule yet!), then the Bastia bus and change as Casamozza for the bus to Calvi, taking about 5 hours total.