I have a dataset containging one minute bid OHLC prices for a particular stock. Would it be reasonable to back test a trading strategy based on this data that only has bid prices? I am asking this since most of the time I see people use last prices (e.g. end of day data from yahoo finance) for the sake of back testing and not just based on bid prices.
I'm a bit confused about what you're referring to in your data. One minute OHLC data is a compilation of the data for that one minute period with the low being the lowest executed price in that minute and the high being the highest executed price in that minute. This has nothing to do with the many, many bid prices that occur in that interval, many of which have no relevance since they aren't actual trades.
Be that as it may, it doesn't matter what you base your backtest on as long as you're consistent. Use only the opens or only the closes, etc. If you find something robust then you can adjust for bid/ask slippage and determine if it's still robust.