Hi

I've done a few obvious searches on SP and the IGI but so far haven't found anything. I can't find any Boullens or close alternatives on the 1841 in Dumfriesshire or, after a quick search, Scotland generally.
I'm assuming that you have the info about his father from a marriage cert. and other info. from this entry in the 1851:
Dykenock, Westlinton, Cumberland
HO107/2428 F 308 Page 7"Mary Irving, hd, unm, 63, farmer of 5 acres emp no labs, b. Cumberland Arthurst (?)
John Irving, son, unm,35, carpenter (master - employing 1 man), b. Cumberland, Kirkington
Edward Boullen, orphan, 13, errand boy, b. Scotland, Gretna
This could imply that he was working for the family or that he was related in some way. it's difficult to tell. I see that John Irving is a carpenter. Have you followed up the Irvings?
I checked for Boullens in Cumberland on the 1841 and found a possible lead:
Ann's Hill, Etterby, Stanwix, Cumberland
HO107/170 Bk 3 F 3 Page 17Charles Graham, 65, Ind,
Ann Graham, 65, b. ? London
Mary Graham, 20,
Mary Campbell, 25, FS
Ellen Boullen, 20, FS, b. ? LondonThomas Athigson (?), 25, MS
all others b. Cumberland.
The ? before London is that both look like London in the County col. but I've not seen it written in like this before.
Ellen seems to be the only Boullen in Cumberland on the 1841. It's worth following her up.
So - possible scenarios ~
Edward was orphaned and was employed by the Irvings - no relationship to them
Edward was a child of a relative of the Irvings
Edward was a child of John Irving (carpenter/joiner) and the mother's surname was Boullen
any others ?
I'll do a bit more searching around later today.
Hopefully some other members might join in the search

Regards
Gadget
Added - alternatives for Boullen:
"Bollin(s), Bulleyn, Bullon, B(o)ullin, Bullant(t), Bullent and Boleyn"