what do you mean a notification? you mean the badge? or are you saying the quick reply comes up AND the stock blue box? details please details, i never changed a thing, im using biteSMS right now and its working perfectly fine.
By default, after installing biteSMS it will over write the inbuilt SMS app notification. If it happens that the inbuilt SMS app giving you notifications instead of biteSMS, then you can go to biteSMS settings and reset all the settings to default, respring your phone and it should be fine.