Leeds/Bradford airport is small compared to Heathrow/Gatwick/Birmingham and their ilk so security checks queues don't tend to be very long. Ryanair will allow you to carry on your handluggage so no bag drop and if you check in online that will speed things up too so 2 hours would probably be more than enough.
Dublin airport is big though, so give yourself plenty of time on the return journey.
JBF one of the destinations from London City Airport is Belfast City Airport or George Best Belfast City Airport as it is officially called . You should try it some time! We have just said goodbye to English visitors who visited N.Ireland for the first time and were delighted with the countryside and Belfast. Helps to have locals to guide you though!! And good weather.
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