Final Fantasy XIV Database - Ffxivpro.com

To unlock trial and nyzul weapons faster I would always sub Corsair to get the Store TP roll which is available at 37, and thus sub-able.

If that's not available sub warrior for double attack. Since you're bard, double march will help speed things up. Try and find someone to help you do some skillchains. Even level 2 SCs significantly cut the time it takes to unlock it compared to soloing one WS at a time.