Before you take that route I'd suggest two different solutions. If you really enjoy a hot mate, I'd recommend to pair a small cup with a lid and a bombilla that can fit through the lid hole. You'll still need to carry a thermos for hot water, but the cup does a great job holding your mate and bombilla securely in a mess free package. And it's not impossible to do the ol' mountain technique with it which is nice. Just prefill the cup with mate, I usually infuse with water while I'm out it, grab your hot water (which can be heating up while doing above steps) and walk out the door with a pretty portable solution.

Second option, is to drink terere from a big cup with a lid and an xl size bombilla. This method allows you to just bring the one cup with mate and ice, and provided there's a source of drinkable liquid near you at work, you can enjoy terere all day. If you access to ice at work even better.