I don't have a definitive answer, but I can perhaps offer some insight. Given the necessary function of rpoA, I would be willing to bet that SigA is the factor responsible for its transcription, so I will focus my discussion there.
Predicting promoters without experimentation can be very challenging given their immense variability. The idealized core promoter consists of a -10 region, a spacer and a -35 region. Recognition of the promoter by a sigma factor is done at the -10 and -35 regions: each sigma factor recognizes a different consensus sequence. Bacillus subtilis SigA recognizes the consensus sequences TTGACA (-35) and TATAAT (-10). They key word there is consensus however, as it is rare that a promoter will actually contain these exact sequences. In reality, 3/6 nucleotides matching could be considered reasonable. Between the -10 and -35 regions is a spacer with conserved length. In the absence of transcription activators, SigA requires a 17 +/- 1 nucleotide spacer. This is due to thermodynamic constraints. Very briefly, promoter melting (at -10) is dependent the angle between the -10 and -35 regions. Given the helical nature of DNA, this angle is in turn dependent on the distance between the -10 and -35 regions. If the angle is just right, the untwisting of the DNA to align the promoter elements and thus allow sigma binding provides the energy to melt the promoter. If the angle is too large, the regions can never align. If the angle is to small, alignment will not provide enough energy for melting. Complicating this are non-standard core promoters and various flanking sequences that all play a role in transcription initiation. As a direct answer to one of your question, a single sigma factor can bind to many different DNA sequences with some conserved regions.
Fortunately, the B. subtilis genome has been sequenced. Your search for the promoter might involve looking for the -10 and -35 regions 5' to the rpoA gene. This however doesn't take into account that rpoA might be part of a polycistronic operon and thus under the control of a promoter further upstream. Suh et al. (1986) did basically this and reported:
Our DNA sequence analysis suggests further experiments to study regulation within the rpoA region. Because inhibition of polycistronic message translation by free protein S4 is one of the chief controls of alpha operon expression in E. coli (16, 23), the apparent absence of S4 from the B. subtilis alpha region suggests different regulation. Although the close coupling of the rpsM and rpsK genes in our sequence (Fig. 3) supports the notion of a translational coupling similar to E. coli, the putative rpoA promoters in the relatively large intercistronic distance following rpsK are also different (28, 29). However, the apparent absence of a rho-independent terminator in this region could indicate that significant transcription occurs from additional upstream promoters in B. subtilis as well as in E. coli (28).
Albeit this is an old paper, but I was unable to find more recent studies in my quick research. Basically they compared the B. subtilis rpoA gene to that of Escherichia coli, where it is located in an operon with ribosomal proteins rpsM, rpsK, rpsD and rplQ (under the control of a single promoter). They found both similarities and differences. They were able to find two possible SigA core promoters in the region between rpoA and rpsK (the next gene 5' to rpoA in B subtilis). There was also a relatively large distance between the two genes, suggesting that they are not part of the same operon. Furthermore, they were able to find a ribosome binding site (Shine-Dalgarno sequence) between the hypothetical promoters and the translation start site. On the other hand there is no transcription terminator between rpsK and rpoA which suggested that a promoter further upstream regulated rpoA expression. After their sequence analysis, they suggested that further experimentation was required.
In conclusion, it's hard to find promoters just by looking at the sequence. Even if you do find a possible promoter, it's impossible to say whether or not it is utilized without experimentation. That said, given that the alpha subunit is necessary for cell function, that the rpoA gene appears to be transcriptionally tied to ribosomal proteins (which are also necessary for cell function) and that SigA is the predominant factor in log phase B. subtilis, I feel that it is very likely that SigA is ultimately the factor responsible for rpoA expression
I also thought I'd mention that there are various online bioinformatics tools that attempt to predict promoters, but I will not comment more on them because I have not used them.