It really depends on the model as to how far west it will be pushed. GFS (7/5, 06 run) is showing that it will recurve on the western edge of the high in about a week, keeping it out to sea. In comparison, NOGAPS (7/5, 00 run) is keeping the high stronger and further west, taking the storm on a track toward Cuba.

This time period is too far out for accurate forecasts though. When you have two of the major models used for global weather forecasting showing completely opposing solutions at that time range, you can pretty much toss both out and say we have no clue what will happen.

About all that I can tell from the models right now is that Bertha is going to maintain Tropical Storm status for the next few days until it hits more favorable solutions, and then possibly intensify.

I think all of us here on the east coast hope the high pressure ridge weakens, as the GFS calls for.

References:
http://moe.met.fsu.edu/tcgengifs/
http://euler.atmos.colostate.edu/~vigh/guidance/