How can we perform the ULS/SLS check after each stage during the Construction Stage Analysis?

You can define the last stage of your bridge with a short duration and name it something appropriate - say 'Completion'. 

And then add one more stage where nothing in the structure changes but it is just the long term duration and name it - say 'Long-term'.

You can then use the Analysis >> Construction Stage Analysis Control >> Final Stage option, to choose up to which stage you want the construction stage analysis to be performed. 

In this way you will not have to change the parameters of your stages later on, but simply change the final stage of your CS analysis based on which case you want to examine.