29P/Schwassmann-Wachmann is an unusual solar system object. Originally classified as a short-period comet, it is now known as a Centaur that recently transferred to its current orbit, and may become a Jupiter family comet. It has exhibited a dust coma for over 90 yr, and regularly undergoes significant dust outbursts. Carbon monoxide is routinely detected in high amounts and is typically assumed to play a large role in generating the quiescent dust coma and outbursts. To test this hypothesis, we completed two three-month-long observing campaigns of the CO J = 2-1 rotational line using the Arizona Radio Observatory 10 m Submillimeter Telescope during 2016 and 2018-2019, and compared the results to visible magnitudes obtained at the same time. As the Centaur approached its 2019 perihelion, the quiescent dust coma grew ∼45% in brightness, while it is unclear whether the quiescent CO production rate also increased. A doubling of the CO production rate on 2016 February 28.6 UT did not trigger an outburst nor a rise in dust production for at least 10 days. Similarly, two dust outbursts occurred in 2018 while CO production continued at quiescent rates. Two other dust outbursts may show gas involvement. The data indicate that CO and dust outbursts are not always well correlated. This may be explained if CO is not always substantially incorporated with the dust component in the nucleus, or if CO is primarily released through a porous material. Additionally, other minor volatiles or physical processes may help generate dust outbursts.