Yes, while the long answer is a little more complicated.
Yes, while some water bottles are recyclable and some are not. Currently, in Canada, there is no universal recycling standard for single-use plastic containers like these- so recycling labels can be difficult to read or misleading. To make it easy on yourself (and the environment) you should invest in a high-quality glass or stainless steel bottle that will last indefinitely- perfect for hot drinks too. The other thing you should start doing is bring your own tumbler cup/ mug instead of buy one at any cafe- this way you cut down on waste and save money too!