Castles & Crusades remains my favorite d20 game, but I've always felt BX still has its place at my table. It just depends on the campaign. I do however vastly prefer the Ability score-based saving throw/skill/everything resolution system from C&C. So let's use it for BX as well! Same Saving Throws, same resolution rules, etc. All we need is to figure out the Target Number (TN) for each Ability Score according to the BX class you chose.
For every method, the TN is determined at Level 1 and remains fixed as the character levels up. Remember that the character is still getting better since in C&C you add your level to saving throws.
For the examples that have to do with BX stats I'll be using the ones found in Old-School Essentials.
Quick Side-Note: Humans get special treatment when it comes to TN Saving Throws in C&C because all the Races need to be balanced with each other. For BX, Humans need no such special considerations as the Saves are attached to a Class, where the XP cost and Level Limits are the balancing factors.
Here are the different ways to do it!
Method One: BX Primes and Non-Primes - This one is very similar to how things work in C&C but keeps that BX flavor for Saving Throw TNs. You choose Two Prime Ability Scores, the others are Non-Prime. (Same for Humans, as mentioned above.) If the Class has Ability Score requirements, you automatically have to choose those as your Primes. The TN for Prime Saving Throws is the lowest number from your BX Saving Throws list. Non-Primes are the highest.
Example 1: A Halfling has to take CON and DEX as their Primes. The TN for those two Abilities will be 8. All others will be 13.
Example 2: An Elf has to take Intelligence as their first Prime, and can then choose whichever other Ability they would like for the 2nd Prime. Prime TNs will be 12, Non-Primes will be 15.
Example 3: A Fighter can put their two Primes wherever they want. Prime TNs are 12, Non-Primes are 16.
Method Two: A Single TN - Note down all your BX Saving Throw scores at level 1 from lowest to highest. The third value is your one single TN for all your Abilities. (Ability Score modifiers will still apply to Saves so there should be some variety anyway.)
Examples: A Thief would have a TN of 14, a Halfling a TN of 10.
Method Three: Assign BX TNs - Note down all your BX Saving Throw scores at level 1 from lowest to highest. Look at the third value and add it one more time to the list. You should then have 6 different values. Assign them freely to your 6 Ability Scores.
Method Four: The SIEGE Engine - "Stop your nonsense, Primes have to be 12, Non-Primes have to be 18! Anything else is BLASPHEMY!" Ok, ok. 12 or 18, the SIEGE Engine. Look at your Saving Throw scores. If you have at least one Save which is 15 or higher, you have Two Primes. If none of your saves are higher than 14, you have Three Primes!
Final comment: Don't forget that the original BX Ability Score Requirements still need to be respected!