That better be a biiiiig bowl. I probably wouldn't do less than 8 gallons for a single fish. 10 or larger would be safer. In terms of space, a tank would be more space efficient which would leave more of your desk for work. According to rough calculations on a spherical bowl, the bowl would have to be 16" tall and 16" wide to have a volume of 8 gallons or more. In comparison, my 7.5 gallon cube tank is 12" tall by 12" wide.
Also keep in mind that shrimp are the bottom of the food chain. Pretty much any fish will take one look at them and see dinner. I'm not saying you can't have both shrimp and fish, but make sure there's tons of hiding spots for the shrimp and let them get established in the tank before introducing any fish.
But as for the question of if you can keep fish in a tank/bowl without a filter, using only live plants- yep. You can do that. Plant that thing up with as many fast growing plants as you can get your hands on. Shrimp don't add too much to the bioload, but stick to only having 1 fish in there.