Your tax home per the IRS is where your regular place of business is, not where you reside. If you are looking to deduct taxes for travel that are work related, the business should be incorporated in a State you would consider or intend to be your office. Being that your business seems to be more online based this maybe difficult. This is a specialized area of practice and your questions are specific so you may want to consult someone in the State your investment property is located or a State you can see incorporating your business.
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You are on the right track. First, you would form a business entity, preferably in the state in which you have the most contact or that you intend as your US office. Then, all business income should be collected by your company, and your business expenses can be paid by your company. This can include your travel expenses if they qualify as legitimate business expenses. (Your attorney or accountant can help with the details of that.)
Your company would then pay you income from the amount left after expenses and other costs. Your income is the part upon which you would personally owe taxes. Your company would also be separately responsible for paying taxes on profits not paid out as income or another purpose, unless you elect to become an S corporation. There is, of course, more to it that will depend on more facts about your situation.
From the information that you have given so far, it appears that forming a business entity would indeed be advantageous. Your attorney will need quite a bit more information to make a definite recommendation.
Disclaimer: Nothing in this post should be construed as legal advice or as creating an attorney-client relationship. Do not rely on the opinions expressed in this post without discussing them with your attorney. Legal advice must be tailored to unique circumstances and this post is for general purposes only.
As a self-employed US attorney practising in the UK, and English notary (a form of lawyer here), I have come across this myself. I understand that you travel to the USA once a year for a month or so and own a rental property there. I presume you then reside in the UK.
You say you are self employed as bloggers and internet marketers. Shouldn't you then already be in business and therefore able to take available deductions?
In any event, as you would be taxable in both the US and UK, and further to the US UK income tax treaty it will do you no good to have the relief in one country and not the other as you effectively pay the higher of the two. You will therefore want to ensure that the same deductions are available in the UK. I have attached a link as to the UK rules as to travel expense which I have attached.
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