I read your query with interest. By this time you may have foun d this information already, but it looks like Andrew H. Ross's parents are Washington and Sidney Ross. Andrew is listed in the 1860 with his mother Sidney in Trappe, so they are free. I think that Sidney achieved her freedom sometime between 1850 and 1858 when Andrew was born so that he was born free. Her husband seems to be Washington Ross, therefore Andrew's father, but he must be enslaved because he doesn't appear until the 1870 census with Sidney in Trappe, Talbot County. In 1870 Andrew, age 13, is a domestic servant in the nearby household of C.E. Flannigan. They live in the neighborhood of the Hughletts - one of the richest and most powerful white families in the region. The Hughletts have a Rachel Ross as a domestic in their household in 1870. Maybe a sister? In order to trace Washington you can check several places. 1st, the tax assessment records for the Hughletts and Flannigains (and nearby slaveholders) in Talbot County for the 1840s-1860s (MD State Archives or they may be still held locally). Many of these tax records list the first and last names of the enslaved. But with a name like Washington, you won't have a hard time finding him as it is not a common Eastern Shore name. Additionally, check the manumission records for the 1850s for Talbot County to see who manumitted Sidney. Check the names of slaveholders in that Trappe, Jamaica Point, etc., area. Through this process you may even be able to find out the names of Andrew's siblings as well as who Sidney's and Washington's parents are.
As far as being related to Harriet Tubman, well, that is more difficult to discern. There are several Ross families in Talbot and I am not clear on how they are related to the Rosses in Dorchester. Harriet's family comes from the Harrisville area south of Madison and Woolford in Dorchester. But you could also be related through marriage to someone you are unaware is also related to Tubman but not a Ross, per se. I believe that Andrew married Emily Catherine Camper, also of Trappe in Talbot. Andrew is married to her in the 1880 census and living in Catherine's mother's home. Seems Catherine Camper Ross is using Emily as her name by 1900. (I suspect a slight census taker error in 1880 with the name.) Anyway, they, as a couple, are consistently in the census. Was Andrew's middle name Harrison? They have a son named Harrison in 1900. Harrison is also a family name for another branch of the Ross family living in East New Market during the 19th and early 20th century. Hope this helps. Best, Kate