BED BUGS or FLEAS

We stayed there for 3 nights, planning on staying for two weeks. The first night I woke up with bites all over my face, chest, and arms and blood stains on the sheets. First I thought they were mosquitoes. The second night my husband and our baby got bites all over their bodies. The host and several of the friends we are traveling with said they were fleas. We moved out of this apartment into a hotel and cleaned all of our stuff and no bites for two nights until last night- some of them got in our luggage and came to the hotel with us despite major cleaning efforts, their are blood stains on our sheets again- definitely seems more like bed bugs!!!
Our trip to Taiwan has been amazing except for this absolute nightmare bug experience.
Other than that, the apartment is beautiful, the hosts are wonderful they were very accommodating in suggesting wonderful things for us to do, everything else that all the reviews say are true but I do not want anyone else to have this horrific experience so I would not recommend staying in this apartment in the near future. I truly believe it's potentially fleas and bed bugs- but we bombed the apartment with all of our stuff in it for fleas before we left. Since some have managed to migrate with us and an the symptoms all point to bed bugs. I wish this nightmare was over, now we need to get rid of these bugs before leaving Taiwan.