Safe and responsible disposal of aluminum chloride?

Sure, you can react the $\ce{AlCl3}$ with $\ce{NaHCO3}$ solution, and you'd also get $\ce{NaCl}$, in addition to $\ce{CO2}$.

Though $\ce{AlCl3}$ is toxic, it reacts readily with water, forming the less toxic chlorohydrate (used in antiperspirants!), and the baking soda should leave an innocuous sludge, safe to dispose of in a sink.

N.B.: The reaction is exothermic and bubbly, so use care when mixing in the $\ce{AlCl3}$ to avoids spatters.

You should begin by consulting the safety data sheet (SDS) provided by the manufacturer and Prudent Practices in the Laboratory to understand the hazards.

The laws of your jurisdiction and the policies of your organization will determine what amount (if any) and by what method neutralization is permitted. Environmental health and safety (EH&S) groups in some organizations deal with authorities who view quenching any regent as illegal unlicensed hazardous waste processing, justifying significant fines. EH&S might insist that you have a special pickup from your hazardous waste provider.

It is possible to quench AlCl₃ cautiously in stirred ice water while keeping the pH to within the permissible range to bulk with your aqueous waste stream. Keep in mind the quench is highly exothermic and can get out of control quickly. From a practical standpoint, the volume of aqueous waste generated might make this approach more costly than having a LabPack pickup of the solid aluminum chloride waste.

On the question "Safe and responsible disposal of aluminum chloride?", I would exercise more care (as to why, see chemistry below) as even neutralizing AlCl3 with NaHCO3 actually, in addition to CO2 and NaCl, may form insoluble aluminum carbonate albeit its apparently breaks down into aluminium hydroxide, if even formed. The latter, however, if improperly disposed of, for example, coming into contact with an organic acid, could potentially reform some soluble $\ce{Al+++}$ ions. Note: Aluminum ions are not found in nature, so living entities really do not known what to do with them. As such, do follow the recommended procedures for the more toxic chemicals.

Does anyone believe there is a problem with aluminum ion exposure? Actually products producing said ions are currently dose limited in Europe where scientists seem to be a little more concerned about possible health effects at higher exposure levels (stating that "Aluminium is a known systemic toxicant at high doses") than say the United States.

But what are the aspects of the chemistry that actually support this cautionary behavior? While the chemistry I present appears to be a little obtuse, it's consequences can be actually rather simply understood. Aluminum ions can capture superoxide radicals and form a weak unstable adjunct compound therewith that, in time, breaks down releasing, unchanged, the superoxide (or in more acidic conditions with a pH under than 4.88, the more powerful $\ce{.HO2}$ radical) to engage in transition metal REDOX reactions. So what actually is the new problem? Well, if superoxide is formed in your lungs because of exposure to transition metals dust and oxygen, for example, it is a transient radical with a limited lifespan. However, upon jumping on board an aluminum ion, it may now have a far greater reach, especially in distant parts of your human body to engage in so-called oxidative stress reactions. Luckily, the superoxide does not live up to its name and it's actually a rather weak radical. However, exposing parts of your brain, for example, to higher doses of any radical activity based oxidative stress damage is not likely healthy. So perhaps not surprisingly, there is a claimed link of aluminum presence to brain disease.

Here is a chemistry based upon a review of two articles noting the pro-oxidant property of the aluminum ion carrying superoxide, which can move transition metals (like Fe, Cu, Mn,..) to lower valence states in Fenton and Fenton like reactions, recycling said reactions, and thereby contributing to so-called oxidative stress related diseases (including Alzheimer's disease,...).

The first alluded to article is “Oxidative Stress Gated by Fenton and Haber Weiss Reactions and Its Association with Alzheimer’s Disease” by Tushar Kanti Das, et al, published in Archives of Neuroscience, July 2014.

Importantly, the work cite, in Figure 4, “Formation of Aluminum Superoxide Semi reduced Radical Ion and Aluminum Superoxide Complex (43)”, with described reactions proceeding as follows (also adopting notation and water complexing from the second article):

$\ce{[Al(H2O)4](3+) + O2•− <-> [Al(O2•−)(H2O)4](2+) }$

$\ce{[Al(O2•−)(H2O)4](2+) + Fe(3+) -> O2 + [Al(H2O)4](3+) + Fe(2+) }$

Note, the above is the usual action (namely, $\ce{O2•− + Fe(3+) -> O2 + Fe(2+) }$ on superoxide recycling ferric to ferrous to promote a Fenton oxidative stress reaction, so, de facto, the superoxide is transported and released courtesy of the superoxide semi-reduced radical ion.

And, at pH < 4.88 :

$\ce{[Al(H2O)4](3+) + O2•− + H+ <-> [Al(O2•−)(H+)H2O)4](3+) }$

$\ce{[Al(O2•−)(H+)H2O)4](3+) + [Al(O2•−)(H+)H2O)4](3+) -> 2 [Al(H2O)4](3+) + H2O2 + O2 }$

Another work: "Pro-oxidant Activity of Aluminum: Stabilization of the Aluminum Superoxide Radical Ion" by J. I. Mujika, F. Ruiperez, I. Infante, J. M. Ugalde, C. Exley, and X. Lopez in J., published in Phys. Chem. A, 2011, 115, 6717–6723, American Chemical Society.

In the Mujika article to quote “In addition, the presence of LMM ligands such as citrate could also have an indirect effect in the oxidation capacity of aluminum by augmenting the bioavailability of Al3+ species, shifting the formation of Al(OH)4- to higher pH’s. However, one should also take into account the effect of citrate chelation itself in the thermodynamic equilibrium of [AlO2•]2+ formation.”

I hope this helps understanding potential issues with Aluminum ions.