The bell jar is symbolic of Esther's mental illness and the way she feels during her breakdown.
I knew I should be grateful to Mrs. Guinea, only I couldn't feel a thing. If Mrs. Guinea had given me a ticket to Europe, or a round-the-world cruise, it wouldn't have made one scrap of difference to me, because wherever I sat -- on the deck of a ship or at a street café in Paris or Bangkok -- I would be sitting under the same glass bell jar, stewing in my own sour air.
The Bell Jar