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Okay, so catching Pokemon in the Safari Zone is actually pretty simple. At the start of every battle, a Pokemon has two counters: the "angry counter" and the "eating counter", both at 0. Whenever you throw Bait, the angry counter is reduced to 0 and the eating counter increases between 1-5, but no more than 255. The opposite happens when a Rock is thrown: the eating counter is reduced to 0 and the angry counter increases between 1-5, but no more than 255.
During the eating mode, the Pokemon's capture rate is halved, while in angry mode, the capture rate is doubled. But the chance of escape is tied to the Pokemon's base Speed. Every turn, a number is generated between 0-255 is generated and if the number is less than half the Pokemon's Speed (in eating mode), double the Pokemon's Speed (in neutral mode), or quadruple the Pokemon's Speed (in angry mode), then the Pokemon will run away. If a Pokemon has more than 128 Speed, it'll run away no matter what, but thankfully the highest Speed you can find here is 110.
So, the best tactic is to throw a Rock and then try your luck, since there's a really good chance you'll catch something. However, if that Pokemon is fast, then there's no point, since they'll have a REALLY good chance of running, but throwing Bait will never help you, unless you really want something to stick around. The problem is you'll never catch it, since those kinds of Pokemon have low catch rates anyway and with no way to inflict status, or lower their health, you won't get a better chance, so either throw a Rock, if they're fairly slow, or just throw a ball and hope for the best. Just never throw Bait.