The Philippines is much friendlier to female foreigners and tourists and less crime than how it's portrayed. For starters, just about everyone speaks english, almost all the signs are in english as well, and that helps a lot just getting around. The main tourist areas are safe, but like any other big city, there are places to avoid. If you're a woman travelling alone from the airport you may want to hire accredited airport taxis to give you peace of mind. For the rest of your transportation while staying in Manila or other major cities in the Philippines, you can rent a car with driver from reputable car rental companies like Dollar Taxi. Travelling by bus, by sea or by plane is by far generally safe in the Philippines. First-class airconditioned bus is a safe bet to travel comfortably as compared to a regular bus. Watch out for overcrowded ship, ferry boat or banca when travelling by sea because driver/operators of these types of transport usually take more passengers than they can safely carry. Same goes with public jeepneys and tricycles. It is very smart to know the local currency conversion to avoid paying too much and avoid ripoffs from unscrupulous drivers.
Foreign women using some common sense should experience little trouble traveling alone in the Philippines. Most Filipinos will be surprised to see a female, especially a foreigner, travel by herself because theirs is a culture that travels in groups. However, your independence will only increase their admiration. Filipinos are generally friendly and helpful.
Local men enjoy whistling and giving out catcalls. No disrepect is meant most of the time. Any response on the woman's part may be seen as an invitation or, more likely, would embarass the perpetrator. Philippine women are wary of traveling alone and may invite themselves to sit next to you on the bus or in the lobby to ward off unwelcome male attention.
Tampons are not easily available so bring your own. The same goes for birth control pills.