We actually do get to find out what is the next step that Biff Loman takes after the discovery of the woman. It is all explained when Bernard tells Willy about the deep change in Biff before and after his surprise visit to Willy in Boston, where Biff went to tell Willy about flunking Math, and his worry about not being admitted at the Univ. of Virginia.
At the time of the visit, Willy was sharing his hotel room with a woman, despite of the fact that he is married. After trying to hide it in many desperate and pathetic ways, Willy had to confess to Biff what was really going on. Biff goes through some logical levels of denial that included silence and shock, until he broke down and cried in pain after having found out what happened. Willy, a very low man indeed, tried to resolve the issue by belittling both the situation and Biff's feelings about it. As a result, Biff never trusted his father again.
We know that Biff' first step was to return and burn the sneakers on which he had sketched the name "University of Virginia". He does this as an act of complete rebelliousness, completely rejecting the dream of football and college fame that Willy had created and forced upon Biff. Next, Biff refused to attend the Math tutoring that he had originally scheduled in order to repeat the Math class and get a second chance. This personal sabotage set himself for failure by losing the opportunity of even being considered to attend UV.
After that, Biff left the family home and ran off to many different places, ending up in a ranch in Texas where he felt quite happy to be doing things of his own initiative. Hence, the next move after discovering his father's affair was to actually cut contact and cease the association with his father.
Now, if we are looking for alternatives as to what actually took place at the hotel room, then we could assume that Biff was so disappointed that he made the decision of never speaking to his father again. In fact, this also happens in the play because Willy and Biff have been estranged for years. Also, when Biff left the home and basically ran away from his family, he did it with the aim of "finding himself". Yet, he never truly finds himself; he only discovers that his entire life has been "a lie" created for him by his own father.
Therefore, Biff did take a series of steps after discovering his father's affair. At the beginning of the play we see that he had just returned after a long time away. He also claims that the house, and its chaos, keeps "calling him back" as if a curse, and that he always ends up there, and still lost. It is the never ending cycle through which dysfunctional families, like the Lomans, always operate.