I obtained a bat model from ebay without a base, so
1)does this need a 40mm base?
2)How best to secure this to the base ?

Yes it does need a 40mm base.
There are several ways to attach it to the base. Even though it is probably metal, you can use a razor blade and cut a tight grid pattern design where the metal meets the base. Then simply apply the glue to the bat and base.
Option two is to buy a hobby drill from army painter supplies. You can get one on ebay for 15 bucks. They are worth the money by far. Drill a whole into the model and the base. Cut a small section off of a paper clip; enough that your newly cut rod connects the model to the base through your drilled wholes. The drilling into the mini doesn't have to be deep. Maybe 1/6 of an inch or so.