The search is the beginning of the Biur. (If one does not search for the chometz one won't be able to burn/get rid of it.) the Bracha he makes is on the whole process of "search and destroy Chometz"
The most critical hefsek is the one between the Bracha and the start of the process. Making sure that the process begins immediately after the Bracha connects the Bracha to the process, which validates the Bracha.
Similarly one may not make a hefsek between making a Bracha and starting the process of eating food on which he made that Bracha. Once he has partaken of some food, he may interrupt, speak get up for a short break and come back, as long as the break is not long enough to be considered to be disassociated with the Bracha. When he determines he is finished his meal (benches or washes may'im achronim, etc) then the eating process has concluded and he may no longer eat without saying a new Bracha.
Here, you make the Bracha on the process of " Search and destroy", start with the search, put the found Chometz away and store it in a bag or collect it to a known place in the morning, setting aside (normally) some food for the morning chometz-dig breakfast. You go back in the morning, eat breakfast, join any left over Chometz to the bag or collection of items found in the search and then burn/get rid of it. This is the end of the process as determined not by each individual but by Chazal, so there is no need to make a new Bracha. See ShA 432/1 and MB (for detail see my comment below)