I do not know about you, but generally, one shower or bath per week is terrible hygiene by today's standards. In fact, anything more than every other day is considered unsanitary. Unfortunately, bathing was not quite as simple during the Elizabethan times as it is today.
Therefore, lower class citizens (making up the bulk of the Elizabethan era people) would maybe only bathe a few times in a single year. For the upper class, they had a little bit more luxury and were able to bathe roughly once every couple of weeks.
The bathing itself was probably not the most sanitary of things. Generally it was taken in an old wooden tub. These tubs were typically placed next to fireplaces so that it would warm the water. However, the water itself was likely fairly dirty.
They did not have treatment plants like they do today. The water that they took baths in was considered unfit to drink. So do you think that a good bath in such water would be very hygienic at all? It probably was not.
Hair itself did receive a little bit better treatment. Unlike today though, they did not have shampoos and conditioners for hair treatment. Typically their hair was washed separately from their bathing and the only thing added was a form of lye soap. This was likely done more frequently among the citizens of the Elizabethan era.
The way of life was pretty unhygienic during Elizabethan period by today's standards. There was no running water, you did not have indoor toilets, and there was no toilet paper. Instead of toilet paper, people would typically use clumps of grass or hay for cleaning.
To top it off London and other places were overly crowded and this made for a huge mess all the time. The unhygienic conditions along with overpopulation is probably what caused the Bubonic plague and other problems to spread so easily from one person to another.