7 days is 0.25 times the twenty-eight days conventionally allowed for a preserved multi-dose vial once it has been entered. Bacteriostatic water is the case that convention was written for. Benzyl alcohol at 0.9 per cent inhibits growth; it does not sterilise, and the twenty-eight days is an assumption about how long inhibition outlasts repeated entry rather than a measurement on your vial. At 7 days you are inside the convention, and what remains variable is the number of punctures on that stopper and whether it was swabbed each time. Growth at the densities that matter is not visible, so inspection is not the check people take it for. Date the vial at first entry and mark the punctures on the label; both cost nothing and both are the evidence you will want later.
The short answer is that bacteriostatic water buys you time in a multi-withdrawal vial — roughly 28 days refrigerated by convention — but it does not make a non-sterile presentation sterile.
Different manufacturers of "bacteriostatic water" vary in their formulation, and some are better than others — brand matters.
The osmolarity of bacteriostatic water is roughly that of normal saline, which makes it generally safe for subcutaneous or parenteral use.
Worth noting that some people have reactions to benzyl alcohol, which is worth knowing if you are going to inject.
Do not use bacteriostatic water as a substitute for aseptic technique.
edited 27 Nov 2024 by s_bhattacharya — fixed an arithmetic slip in the third paragraph