Every group of three symbols should contain at least one 'a' : Following can be the pattern of regex:
$[Xa]^{*}Y$ or, $[\epsilon ,Xa,XaXa,XaXaXa,XaXa....]Y$
Choosing X = Y = $(\epsilon + b + bb)$ , satisfies our requirement.
Otherway, pattern $[Xa]^{*}$ with X = $(\epsilon + b + bb)$ satisfies the required property but these string are always ending with 'a', so concatenate possible valid ending which is Y = $(\epsilon + b + bb)$
I am assuming all strings of length less than 3 are accepted.