The simplest way would be to add a space after your pattern:
$ grep '/aa/bbbb/cccccc ' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
Or, to match all kinds of whitespace:
$ grep '/aa/bbbb/cccccc[[:space:]]' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
Or
$ grep -P '/aa/bbbb/cccccc\s+' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
Or, with a positive lookahead:
$ grep -P '/aa/bbbb/cccccc(?=\s)' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
Or, with a negative lookahead:
$ grep -P '/aa/bbbb/cccccc(?!\S)' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
Or you can reverse the match:
$ grep -v 'c?' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
Or, to also match lines that contain nothing but your pattern (no trailing whitespace):
grep -P '/aa/bbbb/cccccc(\s+|$)' file
grep -E '/aa/bbbb/cccccc(\s+|$)' file
Or, you can just use a small script:
In awk:
$ awk '$3=="/aa/bbbb/cccccc"' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
Or, if you don't know which field your pattern is in
$ awk '{for(i=1;i<=NF;i++){if($i=="/aa/bbbb/cccccc"){print}}}' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899
In Perl
$ perl -ane 'print if grep {$_ eq "/aa/bbbb/cccccc"} @F' file
2014-05-05 09:11:53 /aa/bbbb/cccccc 29899