A significant problem in answering this question is that the outcome you describe ("ruining the relationship") seems like it would be up to your girlfriend's opinions and responses to what you say, which are impossible for us to predict. That said, I will recommend that you involve your girlfriend in drawing up a new household monthly budget (whether you already had one for yourself or not).
You can bring this up very naturally (though I imagine you'll be able to phrase it better :p):
Hey, since our living arrangements are going to be changing soon I thought it would be a good idea to redo the household budget. And since you'll be living here you should have a say in those decisions, too.
The advantages of this approach are that:
- It makes very clear that your costs are increasing as a result of
your girlfriend moving in with you-- more food, household supplies,
sharing of the things you already purchased for yourself, etc.
- It gives your girlfriend an opportunity to offer money, instead of
you asking her for it. She may not do this, of course, but if she
does, then you'll be pretty safe from your relationship being ruined.
- It offers the opportunity for your girlfriend to lay out to you some
of her actual cost of living. Does she like premium bathroom
products, while you prefer cheaper versions? If you share shampoo,
might she go through it at a faster rate than you. You can talk about
that here, rather than after resentment has been simmering for
months.
- It allows you to know what sorts of things you'll need to buy, and in
what amounts, and at what intervals. This takes care of concerns
about you being shoehorned into buying things exclusively for her,
like clothing (I assume you won't share wardrobes), and discuss the
cost of things you'll both use.
- It gives an opportunity to discuss future events (while she's waiting
for her job, this situation will be A, and once she has it the
situation will be B, and when she has to go to school it will be C).
These conversations will likely need to happen anyways, and if you
talk about it now there will be less room for misunderstandings down
the line.
- It prevents miscommunications and mismatched assumptions from
building, then exploding, in the future. Her offer to pay for
electricity and water might seem fine until she sees how much those
actually cost in your home with both of you living there-- maybe you
like long showers, or have a series of BitCoin mining rigs running 24/7, or
whatever. It can be a problem agreeing to pay for a category rather
than paying a specific dollar amount.
- Budgets are about more than required expenses. A good budget includes
categories like savings accounts, retirement funds, emergency liquid
assets, and things like that. You can make explicit that you want,
and intend, to put money towards those things. This might be less
clear if you both just divide strictly necessary expenses.
- You can revisit the budget as needed. It's a document which will
continue to exist, and so if something changes (you use more of some
product than she thought, and she feels the payments are unfair, or
whatever) you can discuss those changes within the framework of the
overall budget rather than getting fixated on individual issues when
they arise (or boil over). You'll both have the same starting point,
which you've both agreed to, for discussion.
After preparing the new budget it will be a lot clearer how expenses will be divided, and you can address any concerns about unequally sharing the burden immediately. If you feel she's not offering enough money, you can point to the budget and show how and where you feel there is a problem and discuss it directly.
As an aside, I'll also recommend not treating your own expenses as necessary and hers as discretionary (e.g., it's true that you'd be paying rent whether she lives with you or not, but only you allowing her to move in with you allows her to escape from that expense for herself). I would presume that if you decided to move in with her she wouldn't offer to take on all of the rent herself, even though it's a symmetrical situation-- in my experience, this type of position tends to be an argument of personal convenience, not enduring principle.
It might be totally fine, but it also might not. If the only kind of relationship she'll accept is one in which you subsidize her lifestyle at the expense of things that are important to you, and you don't want that, then the relationship is unlikely to work out whatever you do. I think you'll both be happier working together with an agreed-upon outlook for your finances.
