I have 3 dogs - 2 bulldogs and a bichon frise. The Bulldogs slobber all over the bichon all day long - he is this white long haired dog. The bichon only gets bathed once a month unless he jumps in the pond - I brush him daily (required for this breed). The Bulldogs only gets bathed once every 2-3 months or so. They get their ears cleaned out only during baths. They don't get their teeth brushed at all (I feed raw). None of them stink. Not even their breath.
So, your dog getting bathed every 2 weeks is not what is causing your bulldog to stink. I am pretty certain your dog has a yeast bloom. A yeast infection can cause that ear to be crusty and stink.
And you can address yeast blooms through diet. What you are looking for is a LOW CARBS diet. Grain free will not help you if the food is still high carbs, but most quality grain free kibble is relatively low carb as well. Yeast thrives on carbs - it's like yummy buffet for yeast fungi. So the more carbs, the more yeast is going to be thriving and happy in your dog. Unfortunately, Carb content is not required in the Guaranteed Analysis label in the kibble bag. So you'll have to apply some math guesstimates. This is how to calculate for Carbs content from what is written on the bag: Carbs % = (100% - Protein % - Fat % - Moisture % - 8%). The 8% there is a guesstimate of Ash content (trace minerals) which is not written on the bag. If Carbs is higher than 50% - you don't want that food, yeast infection or not. But for a yeasty dog, you want that Carbs very low. If you can get it to 0%, so much the better - of course, you will be hard-pressed to find Kibble that is lower than 30% carbs because you need carbs to form the breaded kibbles. If you can transition to wet food or raw feeding then you can go for 0% carbs that way.
There are lots of suggestions above on how to treat Yeast infection - Apple Cider Vinegar bath is a good one. Also adding a little bit of Apple Cider Vinegar to the water your dog drinks - if you can get him to drink it - is also good. But, you still have to tackle the underlying problem to prevent new yeast from living in your dog and not just treat the yeast infection. A visit to the vet is always a good idea.
Hope this helps.