what you require is a pulse oxymeter,this is a special device and as one of the chief designer of Ohmeda inc,i know what is involved,your idea is good and so we placed a bid beyond your budget,
1)it is practically not possible to take oximeter reading from an adult through wrist, finger is the limit,if you want to take from the wrist large power is consumed by the the LEDs and there will be errors.
2)to develop anything on bluetooth is expensive,because you do not get support from the chip manufacturer without buying their development system,the min cost of such system is $3000.
3)PC side is simple,as we have already done it for ECG,oxymeter and blood pressure.