I have not found any article on carbon dioxide removal from air by biofiltration processes such as biotrickling filter or bioscrubber. If any body have some thing in this area please send its link for me. Thank you in advance for you consideration.
Why would a biofilter remove carbon dioxide? A nitrifying biofilter might remove some, because the nitrifying bacteria use inorganic carbon, so there might be some absorption in the water to compensate for alkalinity loss through nitrification.
A bioscrubber will have the same issue - what bacteria do you envisage using carbon dioxide? Really you want a chemical scrubber, and if you search for that you will find plenty.
There are two natural carbon dioxide dioxide bioscrubbers - plants. Photosynthetic activity will take your carbon dioxide and convert it to new plant biomass. I think you may find algae a useful possibility. You will find much material on algal growth rates, from which you can decide if the rates of growth make the process feasible. A quick web search found that this is being proposed for flue gas carbon dioxide removal, so getting support material will not be a problem.