You may be shocked by what I am about to say but vinegar, bicarb, lemons forget it. I'm sorry but in the bathroom I've never found anything that works as well as my cream cleaner and bleach.* I know it's not especially thrifty or great for the environment but in hard water areas these alternatives just don't cut it.
So roll up your sleeves get your favourite cleaner out and scrub!!! Just so your not totally disappointed with this post here are a few everyday cleaning tips for your bathroom.
Begin your cleaning in the bathroom. Spray on your cleaner or disinfectant — which needs time to kill germs — and come back after you've tidied up another room
For the shower - Keep a squeegee and microfibre cloth handy. The squeegee removes "big water"; the microfibre cloth gets those last drops. It'll save you a lot of scrubbing later. Tesco do value micro fibre cloths very cheaply that are perfect for this.
Grout - this is the bain of my life ours permanently looks grotty despite my best efforts but an old toothbrush and plenty of elbow grease do make it look a LOT better. How about doing this whilst you deep condition your hair in the bath?
* with one exception bicarb and vinegar to clean stained toilets, see here.