Banning the Burkini isn't needed for "security reasons" (a justification used for banning the face veil), so it is unnecessary. I think that the ban was more to do with anti-Muslim bigotry than it was with misogyny, as the stated reason was that it showed "affiliation with terrorist groups", when really it's nothing more than religious swimwear. This implies that being a Muslim means that you are affiliated with terrorists.
On one hand, the women who choose to cover their hair are being told what they can and can't wear, which is misogynistic, although I personally don't agree with the hijab and the "purpose" behind it. It is important in a free and democratic society that everyone can wear what they want, be that Dastars for Sikh men, Kippah's for Jewish men or hijabs for Muslim women. On the other hand, the women who do not choose to wear it and only do so due to pressure from their families or communities are being further restricted from fun, leisure activities because there is no way they can go swimming without it.