Just practice stretching exercises. Don't worry about tunes too much at first but try and get one finger one fret if you know what I mean. Index on the F, middle on the F sharp, ring on the G and pinky on the G sharp. Once you can clearly sound each of these notes you are well on your way to mastering the long scale. As you say, plenty players with small hands master the long scale bass. They have just strengthened their hands and practised. I bet in a few days you will be back on here telling us about how you are finding it much easier.