Current New Yorker here! If you need to get to places fast, I would leave buses aside completely - they get stuck in traffic just like cars do and believe me, traffic can be absolutely horrid. Taxis aren't really a good option either for the same reason and also because they're expensive - unless your new company is paying for the fares I wouldn't consider it. Use the subway - it's well connected and trains can't get stuck in the main traffic. You'll get the system quickly and before you know it you'll be a pro at knowing which one to take. And also, make sure you start training for speedwalking soon - everyone in NY seems to always be in a rush so make sure you blend in. Good luck!
