bond - Does the hydrogen ion actually exist?

A chemistry test I did was an IGCSE test. One of the questions was

Is Hydrogen Chloride ionic or covalent?

Now, on a sheet I have been given, it states the hydrogen ion is $\ce{H+}$. So, it forms a positive ion, like metals. I'm fine with that. I know that hydrogen is strange and I also know that the (I)GCSE chemistry curriculum simplifies/lies a lot. The bonding in Hydrogen Chloride is covalent. Now, since a 'Hydrogen ion' is just a proton, I wanted to know whether in reality it actually exists or not.

Answer

Yes free $\ce{H+}$ ions, protons, really exist.

Protons are constantly emanating from the sun and reaching Earth.

The proton flux is continuously monitored by satellite.

However, in a solution such as water, instead of bare $\ce{H+}$ ions, they are $\ce{H3O+}$ or larger ions such as $\ce{H5O2+}$ or $\ce{H9O4+}$.

When $\ce{HCl}$ dissolves, the proton is transferred to a water molecule to form $\ce{H3O+}$.

$\ce{HCl}$ only has 17% ionic character according to Pauling's The Nature of the Chemical Bond, so it is covalent, but reacts with water to form separate ions in solution.

For more information see Eigen or Zundel Ion: News from Calculated and Experimental Photoelectron Spectroscopy:

The appearance of the hydronium ion was and is currently debated as several possible structures, three of them being $\ce{H3O+}$ (the Eigen cation), $\ce{H5O2+}$ (the Zundel cation) and $\ce{H9O4+}$ (the strongly solvated Eigen cation)

and

Both Zundel and Eigen Isomers Contribute to the IR Spectrum of the Gas-Phase $\ce{H9O4+}$ Cluster:

The “Eigen cation”, $\ce{H3O+(H2O)3}$, is the most prevalent protonated water structure in the liquid phase