It was not considered quite proper for "genteel" unmarried young women to travel on public coaches unescorted. Part 5

It was not considered quite proper for "genteel" unmarried young women to travel on public coaches unescorted (Lady Catherine is even more severe: "I cannot bear the idea of two young women travelling post by themselves").

After the marriage proposal from Harris Bigg-Wither Jane announced her change of mind and left the house hurriedly in the Bigg-Wither carriage, accompanied by Cassandra, Alethea and Catherine, fleeing to her brother James and his wife Mary at Steventon. Alethea and Catherine bade a tearful farewell to the Austen sisters; Jane forcefully persuaded James to take her and Cassandra back to Bath the next day, refusing to tell James and Mary what the trouble was. By no way, Jane could have travel alone or with Cassandra, back to Bath. 

One of the most prominent features of the time period was the propriety expected between members of the opposite sex. This was the beginning of the social restrictions that were one of the defining characteristics of the Victorian period, which directly followed the Regency period. A young unmarried women should not be alone with a man without a chaperone; likewise, women were never to travel unescorted.  annemace.net
  

BUT Agnes Grey is traveling alone
 

""But the morning brought a renewal of hope and spirits. I was to depart early, that the conveyance which took me, (a gig, hired from Mr Smith, the draper, grocer, and tea-dealer of the village) might return the same day. I rose, washed, dressed, swallowed a hasty breakfast, received the fond embraces of my father, mother, and sister, kissed the cat, to the great scandal of Sally, the maid, shook hands with her, mounted the gig, drew my veil over my face, and then, but not till then, burst into a flood of tears.

The gig rolled on–I looked back–my dear mother and sister were still standing at the door, looking after me, and waving their adieux: I returned their salute, and prayed God to bless them from my heart: we descended the hill, and I could see them no more""

 

And Anne Bronte was traveling alone
 

Charlotte was traveling alone

 and even talking to a gentleman

Charlotte's return from this short visit to her friend, she travelled with a gentleman in the railway carriage, whose features and bearing betrayed him, in a moment, to be a Frenchman. She ventured to ask him if such was not the case; and, on his admitting it, she further inquired if he had not passed a considerable time in Germany, and was answered that he had; her quick ear detected something of the thick guttural pronunciation, which, Frenchmen say, they are able to discover even in the grandchildren of their countrymen who have lived any time beyond the Rhine. EG-Charlotte

And so her journey back to Haworth, after the rare pleasure of this visit to her friend, was pleasantly beguiled by conversation with the French gentleman; and she arrived at home refreshed and happy.