Is it permissible to use a Siwak stick during the daytime in Ramadan, knowing that some people might experience a little bleeding?

It is permissible for a fasting person to use a miswak and anything that cleans the mouth and teeth. This is supported by the hadith of 'Amir ibn Rabi'ah from his father, who said: "I saw the Messenger of Allah, peace and blessings be upon him, an innumerable number of times using the miswak while he was fasting." The emission of blood when using the miswak does not invalidate the fast.