This is the bidet model I've used
MB110As for a cost analysis... I'm going to have to do some approximations, but here is a quick guess:
The model I use does not heat the water, so I'll not factor that in for now. The bidet uses approximately 1/8th a gallon per use. With the national average for water costs being ~$2/1000 gallons, this works out to $0.00025 per use of the bidet.
I save approximately 8 squares (just a WAG) per use. My toilet paper costs $.75 per roll and the roll has 176 squares (yeah, I know we should buy less expensive TP, but sometimes quality matters). This works out to $0.03409 savings per use. So subtracting the water cost, the bidet would seem to save $.03384 per use.
There are two people in my house and the we each use it about once a day. so the annual savings should be $24.72.
It took me about an hour to install, and it is slightly harder to clean the toilet since you have to clean around the nozzle. I would put the extra effort at 15 seconds a week or 13 minutes a year. Using $25 / hour this works out to an additional $25 up front and $5.42 per year.
So, initial cost for us was $65 with installation, and we save 20.30 dollars per year factoring in the extra cleaning time. Breaking even in a little over 3 years.
Not the best ROI, but I would hope to get at least 6 years out of my bidet and save a little money. There is also the benefit of not wasting the resources associated with TP, and the hygiene. The numbers will obviously be different for different bidet models and households.