In 1840 they were in Addison, Gallia Co., OH. with one male under 5 (b1835-1840), one male 30-40 (b1800-1810), 1 female under 5 (b1835-1840), 2 females 5-10 (b1830-1835) and one female 20-30 (b1810-1820). The record has been transcribed "Richard Bunes."
The 1830 census for Freedom Twp., Cattaraugus Co., NY also has a Richard "Bunts" with two males under 5 (b1825-1830), one male 5-10 (b1820-1825), and one male 30-40 (b 1790-1800).
There is also a James Bunts in Randolph Twp., Cattaraugus Co., NY with one male 30-40 and one female 30-40 (each b1790-1800).
Although the Richard who was in Gallia Co. in 1840 and the Richard in Cattaraugus Co. in 1830 don't add up to the exact ages of the children, that isn't unusual. Trying to fit your children into the age brackets while a census taker twiddled their thumbs wasn't easy.
I did not find a marriage record anywhere for Richard and his wife, and no death record for him.
There is a Richard Bunce (03 Aug 1796-03 Sep 1873) buried in Poplar Ridge Cemetery in Gallia Co., OH but his wife was named Mary J. (1819-1898). Her tombstone is inscribed "wife of Richard." I thought I was onto something. That led me to further research which showed that this Richard and Mary J. (nee Williamson) Bunce were from Mason Co., WV.
I'm sorry but there are just no more records.