A few brief comments on the street constituted the extent of a proper period of conversational exchange. An outright refusal to allow the gentleman to accompany the lady would be rude, and even declining the request in a gentler, but still direct form might be considered something of an offense. The lady could certainly proffer an excuse that she had matters to which she must attend alone, though, without giving offense. That response should be sufficient to any gentleman to let him know that his presence was not required and perhaps would be inappropriate or unwanted for the time being. Whether she accepts his company or not, her answer should be given both quietly and with grace.
Ladies are never to be loud, and never to be unmannerly.
Should the gentleman walk along with the lady, it is his duty to accommodate his speed to match the speed of the lady. The onus is upon the gentleman to keep a conversation brief. He will know that it is acceptable to continue the conversation after he excuses himself only if the lady asks him to please continue with her. Again, to protect against even the appearance of impropriety, if the gentleman lacks the good manners to bring the conversation to a close when he should, the lady will then have to take it upon herself to end the conversation. Even when a lady knows and speaks with more than one man, it is improper for her to take the arm of two men flanking her at the same time.