Fortunately for us, the narrator of Unbearable Lightness likes to analyze his own novel. He tells us what the bowler hat signifies over the course of several philosophy-heavy pages. We'll give you the highlights and discuss each one:
It signified violence; violence against Sabina, against her dignity as a woman. […] The lingerie enhanced the charm of her femininity, while the hard masculine hat denied it, violated and ridiculed it. The fact that Tomas stood beside her fully dressed meant that the essence of what they both saw was far from good clean fun […]; it was humiliation. (3.2.3)
There is a lot of discussion of sexual humiliation in Unbearable Lightness, and by the end of the novel we see that both Tereza and Sabina harbor a secret desire to be degraded by the men with whom they have sex. (After having sex with the engineer, Tereza wants him to watch her go to the bathroom; Sabina has the same desire after making love with Tomas. This is another example of the continuity achieved through the iteration of specific words and phrases, as discussed in "Writing Style.") The bowler hat is not only a symbol of sexual degradation, but a reminder that such degradation is voluntary, in fact longed for, by the women in this novel.
It was a memento of her father. After the funeral her brother appropriated all their parents' property, and she, refusing out of sovereign contempt to fight for her rights, announced sarcastically that she was taking the bowler hat as her sole inheritance. (3.2.6)
Sabina's relationship with her father is complicated. The basic deal is that much of her life has been about betraying her father and the ideas (the kitsch) he tried to instill in her as a child. By refusing to fight for her inheritance, Sabina renewed her betrayal and abandonment of her father. In this way, the bowler hat symbolizes her love of betrayal.
It was a sign of her originality, which she consciously cultivated. She could not take much with her when she emigrated, and taking this bulky, impractical thing meant giving up other, more practical ones. (3.2.8)
This follows from our previous comments on Sabina's attraction to betrayal and her lifelong fight against kitsch. Later in the novel, when kitsch is discussed in gory detail, we learn that the individual who insists on his individuality is the enemy of kitsch, because kitsch forces conformity on its followers. If the hat is a symbol of her originality, then it is also a reminder that Sabina's enemy is kitsch.
It was a vague reminder of a forgotten grandfather, the mayor of a small Bohemian town during the nineteenth century. (3.2.5)
It was a recapitulation of time, a hymn to their common past, a sentimental summary of an unsentimental story that was disappearing in the distance. (3.2.9)
The bowler hat was a motif in the musical composition that was Sabina's life. It returned again and again, each time with a different meaning, […] though all former meanings would resonate […] together with the new one. (3.2.10)
This is where the bowler hat gets really interesting. First, the mention of Sabina's grandfather reminds of us Tereza's own anachronisms (yet another example of strategic repetition on the part of the narrator). Moreover, it sends us back to the idea of eternal return and a cyclical version of time in which events – or in this case, an object – is repeated ad infinitum. Because the bowler hat is repeated over and over again, it has weight or significance (see "What's Up with the Title?" for the philosophic reasoning behind this). Most importantly, these passages introduce an important concept in Unbearable Lightness of Being – motifs. Read on for more.