It’s hard to say definitively one way or the other. I am of two minds on this issue and will present both sides of the argument.
Argument for recycling: Studies have shown that people do not wash reusable bottles well enough for them to be safe from bacteria such as e coli which can cause serious health problems such as urinary tract infection, giardia which causes diarrhoea and vomiting, and campylobacter if it is contaminated with milk. Reusable water bottles can also come in contact with chemicals like phthalates, BPA (bisphenol-A), and cadmium, which some research groups believe contribute to increased rates of cancer and other diseases like developmental disorders.