Do the following inexpensive & simple steps to solve your problem:
1. Strip (1/2") the ends of your battery clip leads & tin them with solder.
2. Strip (1/2") all ends of 2 insulated (1"L x 20 AWG) solid copper wires & insert them into your breadboard power rails.
3. Buy/Make 2 (stranded-wire) jumper wires with boot-insulated alligator clips on each end (i.e. 2 wires & 4 clips--whatever length you want).
4. Clip the alligator clips to the battery clip wires & when you want to power your breadboard, just clip the other alligator clips to your breadboard power rail wires.
Alternatively, you could do the following instead:
1. Strip (1/2") the ends of your battery clip leads & tin them with solder.
2. Strip (1/2") all ends of 2 insulated (6"L x 20 AWG) solid copper wires.
3. Solder one side of the solid copper wires to your battery clip wires.
4. When you want to power your breadboard, just insert the other ends of the stripped solid copper wires into your breadboard power rail.
Or, simplest of all, you could do the following instead:
1. Strip (1/2") the ends of your battery clip leads & tin them with solder.
Tinning the wires makes stranded wires quite inflexible--but be careful when inserting them--the point where the tin approaches the insulation is vulnerable to stress & can weaken stranded wires over time.
HTH
Best Regards!