Well, from my point of view, as nowadays I play bass more than the guitar (there are just a few bass players and sooo many guitarists…) in bands and as I tried a lot of bassists to play with… there are several things.
First of all, the most important thing as for almost every band member, it’s personality of the bassist. If you cannost get along, it does not matter how good he is, it simply would not work with a person who for example does not communicate, behaves in a strange way or is always late for no reason without any explanation or apologie. And that is general for everyone, not only for bassists.
Another thing, do you play covers or your own songs? If you are a cover band or if you have several songs written, select a few songs, send him what is needed and get a time estimation.
Another very interesting way how to test a bassist coming to a band with their own songs (and I have been tested like this) is working only when you don’t have any records or you are willing to let him express himself. Just let him come to the rehearsal, pick a song, play and try to let him ‘fall into it’. Then you can find how he can accomodate, if his playing goes along with the band etc… but, if you have some vision about the bass line, be opened, tell him, but don’t be stubborn – you want to get a new member that might be with you for quite some time. However he should be opened as well and don’t worry to tell him if you do not feel like he’s the right one. Give it some time, maybe even two or three rehearsals. After this time you should be clear to tell whether he’s good for your band and also for him to find out if he wanna continue. These things simply cannot be seen from the first rehearsal.
Hope it helps you and good luck!