You want to change something that is normally the responsibility of others in your company, and others may have a different view on that - or have already evaluated and discarded it. So threadtread lightly, it is easy to offend others if you attempt to change your organisation. That said, I don´t want do discourage you to take action just warn you: It is going to involve more than just adding a few containers.
If you really want to make this happen, find out who is responsible for office management / furniture / waste disposal because this is not normally an HR-responsibility. Try to get in touch with them and have an informal chat where you probe the situation. Hint that you would like to see more recycling bins and see how they react. If he/she is somewhat open you can volunteer to support, but don´t take away their responsibility.
Another option could be to draft a decision proposal to the responsible manager. It should contain a good overview of costs, benefits and risk and be neutral as in: Hey, I have a suggestion. Maybe you find it helpful. If you decide to act on it, I am happy to support this. If not, no big deal.
In any event, be prepared for very frustrating reasons why nothing can be changed...
