Allah knows best - and it seems that gum bleed doesn't break wudu. Prophet Muhammad, Peace be upon him, said https://sunnah.com/tirmidhi:22:
"If it were not that it would be difficult on my nation, then I would have ordered them to use the Siwak for each prayer."
What we learn from this is that this is extremely recommended. This can be classified under, considering the strength of the wording of recommandation in hadith, "Wajib minus punishment for not doing it".
So we would all be doing it if we had the same piety standards as our Prophet, Peace be upon him, or maybe as much as the Companions. For every prayer.
We also have clear evidence that our Prophet, Peace be upon him, sometimes prayed multiple fardh prayers with the same wudu.
Therefore even if blood would invalidate wudu (about which I have no idea), the blood from gums is forgiven, because only few people can apply miswak many times without never having gum bleed.
But furthermore as Hanbali scholars considered, none of the many companions is ever reported to ask about blood, and they were correct to be shy to ask too many questions, it's unlikely to have none of them ever bleed, because that's hard to do, especially before this modern age. So to conclude, minor bleedings are forgiven. And this is reliable view, because silence in Qur'an and Sunnah is a well-known mercy of forgiveness.
”. It's also reported that he (PBUH) said: “Al-Halal (the Lawful) is what Allah has made lawful in His Book, and Al-Haram (the unlawful) is what Allah has made unlawful (forbidden) in His Book, and on what Allah is silent, is something He has excluded (forgiven), so you should accept from Allah His exclusion (forgiveness)”.