There are two measurements you need: shell width and axle length.
Shell width is very easily determined - you can just measure it. The standard for road bikes with threaded bottom bracket shells is 68mm but some gravel bikes use 73 so it's worth checking.
The axle length can also be measured but you need to at least pull the cranks off to do so.
Different model cranks require different axle lengths to get the correct chainline. Shimano publishes detailed specifications going back to 2005 that will tell you what BB you need for any of their square taper cranks, but as you have an FSA crank that does not help. FSA does publish some documentation if you dig for it a bit. The manual for the current version of the Vero crank is here. It gives a FSA BB part number, the notes say '110.5 for Chainline 44' - i.e. 110.5mm axle for 44mm chainline - which is correct for a road double drivetrain.
Looks like you are correct and a 68x110 BB will be fine.