There are really no set rules defined for how to handle this situation. As long as you keep track of how you allocated things between State A and State B and remain consistent, then any method you choose should work.
That being said, you could either just report your State B income on the State B return or adjust the income for the travel expenses to go to that job site.
To take it a step further, if your income from State B is a significant portion of your total income, you could also attribute a proportional amount of other expenses to State B (without taking the home office into account). It may not be worth the time and effort to allocate the expenses between the two states if the income from State B is not very large compared to your total income.
@J9999
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