Elizabeth very rationally thinks it is highly improbable that Jane should meet with Mr. Bingley while in London with their aunt and uncle Gardiner; however, she has not entirely let go of the hope that Jane might see him.
As Elizabeth explains to her aunt Gardiner, it is so extremely unlikely that Jane should see Bingley due to the part of London that the Gardiners live in. The Gardiners live on Gracechurch Street in Cheapside, the business district of London, while Bingley and Darcy live in the wealthier more fashionable side of town. Since Bingley is with Darcy, Elizabeth knows that Darcy would never condescend to allow Bingley to call on Jane in such an unfashionable part of London. As Elizabeth phrases it, "Mr. Darcy would no more suffer him to call on Jane in such a part of London--!" (Ch. 25). Elizabeth further proclaims with her characteristic wit that "Mr. Darcy may perhaps have heard of such a place as Gracechurch Street, but he would hardly think a month's ablution enough to cleanse him from its impurities" (Ch. 25). Furthermore, since Bingley never ventures anywhere without Darcy, Bingley would also never go to Gracechurch Street.
However, Elizabeth is allowing herself to hope. Despite the fact that Mrs. Gardiner thinks that Bingley's attraction for Jane may not have actually been very sincere and deep, but rather the typical fleeting fancies of a fickle young man, Elizabeth still wishes to believe that the feelings she saw Bingley express towards Jane were sincere. Therefore, she is allowing herself to hope that if Bingley learns from Caroline Bingley that Jane is in town, then his affection for Jane "might be re-animated," and then he may decide to escape his friends' influence and call upon Jane at Gracechurch Street himself.