Copper sulfate reacts with sodium bicarbonate reacts to form basic copper carbonate due to the great affinity of the $\ce{Cu^2+}$ ion for the hydroxide anion $\ce{OH−}$. From its Wikipedia article:
Basic copper carbonate can also be prepared by reacting aqueous
solutions of copper(II) sulfate and sodium bicarbonate at ambient
conditions. Basic copper carbonate precipitates from the solution,
again with release of carbon dioxide:
$$\ce{2 CuSO4 + 4 NaHCO3 → Cu2(OH)2CO3 + 2 Na2SO4 + 3 CO2 + H2O}$$
Here, the "ambient condition" is very important because if we alter the temperature and/or pressure , the reaction may tend to form copper(II) carbonate or any non-stoichiometric copper compound.
Heating the basic carbonate in an atmosphere of carbon dioxide (produced by the decomposition of silver oxalate at 500 °C) produces copper(II) carbonate but it is itself quite unstable and react with moisture to convert back to basic carbonate.
For advanced reading, you can refer to reference 2 below in the reference which describes Copper/bicarbonate equilibria in solutions of bicarbonate ion in details (which clearly shows formation of basic ion $\ce{CuCO3(OH)^2-}$ in the solution).
Notes and References
- http://www.sciencemadness.org/talk/viewthread.php?tid=24056
- https://www.sciencedirect.com/science/article/abs/pii/0043135471900492
- http://science.wonderhowto.com/how-to/synthesize-copper-ii-carbonate-sodium-bicarbonate-302466/ (Although this site claims to make copper(II) carbonate, it is actually making the basic carbonate. You can clearly see its bluish green color of basic copper carbonate).