Bastet doesn't have one particular build, though there are some items you want to build just about every game. I'll go over the offensive and defensive items, along with actives, and what you shouldn't be building.
Absolute best item you can buy on Bastet. Since she's so mana starving this item saves your life, with damage to boot.(With my build, you'll have 2195 Mana[3% of your mana is converted into damage, being 65.85 extra damage on this item])
Cooldown, damage, penetration, and extra mana for Trans and Bastets Mana thirst, what's not to love? Wanna rush this after Trans and boots.
More physical power, and penetration. Pretty simple, make it hurt.
Move fast, get power, standard stuff. Since Bastet is mobile on her own, you don't actually have to rush into these honestly.
^^^^^^ These are items you will ALWAYS build ^^^^^^^
Defensive Pickups
When you hit your Titans Bane, this is your power spike. You have plenty of damage, and can opt. for defensive items, all depending on the matchup.
Probably the best item to pick up after Titans Bane if all is going well. Gives protections and extra damage, since you never want to lose much damage when you opt. defense items.
This item saves lives. It was nerfed, but still saves lives. You want this if they have CC, duh.(Ymir, Nox, Athena, Ares; Anything that will guarantee your death.)
This item is extremely underrated honestly. I build this if there's a fed Mage(And only then, or if you find yourself hurting from a magic damage source) 15% Cooldown, 250 Bonus HP at max stacks 40% magical protection, and 25 physical damage. Like I said after your main four items, you can opt this without losing much.
I only build this against Loki so he can't 1 shot me
Really Niche item like Hide, I only get this if there's a huge amount of damage coming out of Magicals that's constantly life threatening.
Others
I personally don't build this, nor have I ever. It got nerfed decently enough to make it not worth it imo.
If your teams heavy and you find yourself losing, don't forget you have a huge amount of split push potential with your ult. With this and even faster.
Actives
Best active for Bastet. CC is GG when it comes to Bastet, any outs will help you.
Curse is more of a team oriented pick up, or if they have a problematic healer(s). Also good if they have Mercury or a auto attack based hyper carry.
I don't usually get this item honestly. It's alright early but other actives are better.
This item offers you a lot of outplay potential. You want to use this if you're an aggressive player. You can get away from dives with this, you can use it to stall for Pounce cooldown, and you can use it to avoid ults.
This item is pretty self explanatory, deflect damage back. Works in some instances.
Saying it's weak early since they nerfed their health level 1. It's all about using it right, you can't just throw level 1 cats out.
It doesn't scale a lot so, it got nerfed but it stills 3 x 500hp hp which can take a lot of tower shots.
In late game cats don't get a better utility IMO.
I don't really agree with the cont. "Ult is weak early". Bastet cats got a lot of Hp in early game, mostly any god would die before killing them, also most of bastet use their lvl 5 reach to gank mid and even try to dive him letting the cats tank the tower, so them will hold a few shots, so i disagree, for me one of most strongest ults in early game, also it's backdoor potential it's insane.
Saying it's weak early since they nerfed their health level 1. It's all about using it right, you can't just throw level 1 cats out.