If you are doing estrogen bloods and you are peri, you need it to be around day 3 - preferably during your period. This is when your own estrogen will be lowest and you will get the clearest sign of what you are getting from HRT. It makes a huge difference. And do this for every set of bloods for consistency.
In terms of taking estrogen on the day, if you are on gels, don't put any on until after your bloods are done. Go home and put it on then. If you are on patches, make sure it isn't a patch-change day but is roughly in the middle of a patch.