Construct a grammar for the language
The string much start with $ bb $ . 
There should at least one occurrence of the sub-string $ bab $


Hence, the structure of the regular expression must be something like this:
$$ bb[some \: string]bab[some \: string] $$

and, we can define $ [some \: string] $ something like this:

$$ (a + b)^* $$

which means, there can be any number (including 0) of either a's or b's.
Therefore, the final regex for the word is, 
$$ bb(a+b)^*bab(a+b)^* $$