Bathroom light has to be switched on twice to work
Pull chain switches have a rotating contact plate; each time you pull it it spins the plate and alternates between no-contact/contact-1/no-contact/contact-2/no-contact/contact-3 (the numbers are hypothetical, different switches have different numbers of contacts...). I suspect that one of the contact positions is dodgy (corroded terminal, bent contact blade, etc.)
You need a new switch.