Hmmm, watch out double quotes could lead to problems if you had other variable-looking items, e.g. those prepended by a sigill ($,%,@,&,etc.) in your string and perl would want to interpolate them too! If they happen to exist, perl would be eager to replace them, if they do not exist perl will replace them with empty unless you used use strict; use warnings;
Why don't you build your $bfquery as a sequence of string concatenations using single quotes or variable contents, for example:
$bfquery=
# this is a string in single quotes so nothing is interpolated
'query?relevance=%28names%20of%20it%2C%20ip%20addresses%20of%20it
+%2C%20root%20server%20of%20it%2C%20operating%20systems%20of%20it%2C%2
+0
last%20report%20time%20of%20it%2C%20agent%20versions%20of%20it%2C%20va
+lues%20of%20results%20from%20%28BES%20Property%20%22_SupportGroup%22%
+29%20of%20it%29%20of%20bes%20
computers%20whose%20%28%20name%20of%20it%20as%20lowercase%20starts%20w
+ith%20%22'
# add to this the value of this perl variable
. $bfcomputer
# and also this fixed string
. '%22%29'
# end of concatenation
;