I think if you take it literally, it means it's not VERY old, but it's slightly older than you would like. So I would say that if something is "a bit too old", then it's not as old as something which is "too old", since it's only "too old" by a small amount.
If the house is very very old, then you could say, "the house is much too old" or "the house is far too old", or very informally, "the house is way too old". The last one is colloquial, so you can use it with friends and family, but not in business meetings!
So, in order of oldness:
The house is brand new.
The house is a bit too old.
The house is too old.
The house is far/much/way too old.
This is very literal though, and sometimes people will be a bit sarcastic and say "...I think the house is a bit too old, don't you?", which would probably be more equivalent to "the house is way too old", but it's cheeky. Don't worry about that though, just look out for the tone and facial expression.