Should I be worried and if so what should I be checking?
Yes,
When running the lathe for a period, check for temperature over the bushes, particularly the unit not using oil. Any warmer than blood heat needs investigating.
Check the bush that is losing oil and determine where the oil is going. If you see oil escaping from the oilite bush and dribbling down the countershaft leg, the oilite bush will need to be replaced before damage is done to the countershaft spindle. The bushes are cheap (shop around the online bearing resellers of buy at a premium from Myford), the spindle is a v expensive component.
Check the bearing that is apparently using no oil as detailed in above posts. A bush in good condition will not be using use much oil – perhaps a slight top up after an hour or two of running. If this is not the case then check the oilway has no waxed or solidified oil. If oilway clear, it is possible that oil has solidified in the pores of the sintered bush. In which case I would replace the bush for the reasons given in the above paragraph.
The bushes are replaceable without taking the whole countershaft off the machine, but you will need to make some pullers using threaded rods and tube and some dies (piece of ally turned to od of .75in with wider section aprox 15/16 to extract and insert the bushes. It is important to completely fit the replacement bush with an accurately turned .75 in pin when pulling the new bush in, if you don't, you may distort the bush and not be able to get the countershaft spindle back in again.
I have a similar problem – one bush is actually OK but since I have to take the spindle out, it is expedient to replace both.