They will have sanitizer and a bottle brush at the home brew. If there is nasty build up a soak in toliet bowl cleaner first helps. Nasty stuff eye protection and gloves.
Carefull with the dishwasher. Not sure it will get the insides clean and the heat may break the bottles. Let us know how it goes.
I have some sanitizer and a bottle brush for my home brew ( root beer) kit, so after a spin in the dishwasher I will sanitize them and wash again. I have a dishwasher that does not use a heating coil so I'm not too worried about running them through it.