Must every TVS have a bounded set?

Question

I have little knowledge in the area of topological vector spaces, so this question may sound very ignorant. But must every TVS possess a bounded set? What I want to prove (or disprove) is that if $f$ is a bounded linear map between two TVS, then there is an nbd of $0$ in the domain space, where $f$ is bounded. This will be achieved if there always exists a bounded set in a TVS.