Firstly - beware!
Buying a house to 'do up' may not necessarily produce a profit. And any profit you make, unless you are also living in the house, you will have to take out of that the cost of all the loans etc. Make sure you can afford to take the 'hit' of a loss before going ahead with the venture.
Now to your question. Yes, bridging loans are more expensive because a) they may not be secured on a property and more risky to the lender, and b) the lender has to make his profit over a shorter period of time as such a loan by its nature should not last long.
So are you looking at owning 2 houses at the same time - I am confused? Or are you looking at doing up the first house, making a profit, and buying your 'real' house with the, hopefully, profits?
Assuming the latter, then the question makes little sense as should you sell the property, you would have to pay back any mortgage you have secured on that property. (That is the whole point of a mortgage - if you default, they sell your house to pay off the loan. When you sell the house, the lender makes you have to clear the loan/mortgage otherwise they would be left lending you money with no way of getting it back should you default.)
Please clarify!