I have no experience researching the HBB gene, but as you have no answers so far maybe this will help (or at least help clarify your question):
I supplied a link to a (not very new) paper that gives a detailed analysis of the HBB promoter region. According to the publication, the HBB promotor is directly upstream of the HBB gene.
I also supplied a link that should load the UCSC browser at that position. Note: I set to hg19 reference genome because that is what is used in the paper, but the sequence in not reversed like in the paper, so it is left-to-right in the link. If you want it exactly like in the paper, just click "reverse" under the genome browser window.
Maybe someone with more experience with HBB can add on to this and provide some more up-to-date publications.