NEt64, as chrisboy said, you would have to take into account the cost of installing the electric shower. Speaking from my point of view and based on the information you have provided, I am not sure you are doing anything "wrong" to be honest.
You said that you do not have gas, just electricity so think about it. This bill is for about 2 months I assume. For that amount you get:
Heat
Hot water
Washing machine (min once a day)
Dryer (min once a day)
Fridge
Hob
Oven
Computer and possibly printer
TV's, Dvd and any other kind of audio/video equipment
Lighting
All that for 5 people? I think you are actually doing quite well. I, at first, thought, that you also had gas...As I have mentioned, our bill came in yesterday and was about 240 euro and there is only 2 of us. We don't waste energy, don't leave lights on when we are not in a room, we unplug TVs, only use the dryer occasionally but for two months and ensuring that the place is nice and warm, I think it is ok. So, I honestly don't think there is something wrong there.
If compared to last year, your bills this year will be higher given the hikes in prices. As for your neighbour, who knows, maybe she does not keep her house as warm as your house? maybe she does not use her washhing machine/dryer every day? or Maybe she has a tip she could share with you?