This shouldn't normally happen as BM correctly installs and removes its traffic filtering driver. It never happens on a clean system installation.
However, there's a slim chance of a problem if you have other products that install similar drivers, e.g. a firewall or antivirus software. In this case, the product with the similar driver needs to be reinstalled after you uninstall BM. Though it is probably easier to leave BM installed and keep things working.
Alright, so I had this exact problem on my new Windows 10 computer when I accidentally installed the Bandwidth Manager (still not sure what it does, was here for Networx). I had to reinstall it before I had internet connection back, however I figured out a workaround to actually uninstall that is relatively simple.
I uninstalled BM via the Add of Remove Programs settings in the new Windows 10 Settings thing initially, leading to this problem, but later I uninstalled via the standard control panel option found in older versions of Windows (change or remove a program in the search bar). Internet was still working when I did this.
As a side note, at the time I was only using the default Windows Defender and Firewall and the only other programs that reasonably could be related to the program were BitComet and perhaps Networx (all the rest did not connect to the internet, besides maybe updates)