You will need to use BCP with a format file. That way you can specify which columns are quoted and which are not. The format file has a way to specify each column, including separate delimiters which is the case when you have quoted columns.

edit: actually I may have misunderstood you dilemma also. If some columns have quotes and others don't, I would suggest reformatting the file to strip the quotes and replace the column delimiter with something else ( like pipe or any other character that would not show up in any of the columns). I have done this in the past and it works well. It does require to write a simple reformatting utility in .NET or some other scripting language but that's pretty simple.