We study color allowed bottom baryon to $s$-wave and $p$-wave charmed baryon non-leptonic decays in this work. The charmed baryons include spin-1/2 and spin-3/2 states. Explicitly, we consider $\Lambda_b\to \Lambda^{(*,**)}_c M^-$, $\Xi_b\to\Xi_c^{(**)} M^-$ and $\Omega_b\to\Omega^{(*,**)}_c M^-$ decays with $M=\pi, K, \rho, K^*, a_1, D, D_s, D^*, D^*_s$, $\Lambda^{(*,**)}_c$ $=\Lambda_c$, $\Lambda_c(2595)$, $\Lambda_c(2625)$, $\Lambda_c(2765)$, $\Lambda_c(2940)$, $\Xi_c^{(**)}=$ $\Xi_c$, $\Xi_c(2790)$, $\Xi_c(2815)$ and $\Omega^{(*,**)}_c=$ $\Omega_c$, $\Omega_c(2770)$, $\Omega_c(3050)$, $\Omega_c(3090)$, $\Omega_c(3120)$. There are six types of transitions, namely, (i) ${\cal B}_b({\bf \bar 3_f},1/2^+)$ to ${\cal B}_c({\bf \bar 3_f},1/2^+)$, (ii) ${\cal B}_b({\bf 6_f},1/2^+)$ to ${\cal B}_c({\bf 6_f},1/2^+)$, (iii) ${\cal B}_b({\bf 6_f},1/2^+)$ to ${\cal B}_c({\bf 6_f},3/2^+)$, (iv) ${\cal B}_b({\bf 6_f},1/2^+)$ to ${\cal B}_c({\bf 6_f},3/2^-)$, (v) ${\cal B}_b({\bf \bar 3_f},1/2^+)$ to ${\cal B}_c({\bf \bar 3_f},1/2^-)$, and (vi) ${\cal B}_b(\bar {\bf 3_f},1/2^+)$ to ${\cal B}_c({\bf 6_f},3/2^-)$ transitions. Types (i) to (iii) involve spin 1/2 and 3/2 $s$-wave charmed baryons, while types (iv) to (vi) involve spin 1/2 and 3/2 $p$-wave charmed baryons. The light diquarks are spectating in these transitions. The transition form factors are calculated in the light-front quark model approach. All of the form factors in the $1/2\to 1/2$ and $1/2 \to 3/2$ transitions are extracted, and they are found to reasonably satisfy the relations obtained in the heavy quark limit, as we are using heavy but finite $m_b$ and $m_c$. Using na\"{i}ve factorization, decay rates and up-down asymmetries of the above modes are predicted and can be checked experimentally. The study on these decay modes may shed light on the quantum numbers of $\Lambda_c(2765)$, $\Lambda_c(2940)$, $\Omega_c(3050)$, $\Omega_c(3090)$ and $\Omega_c(3120)$.