Sort entries in a category via entry field
You are getting this error because the "entries" fields are always considered to be a query (ElementCriteriaModel) that can return more than one element. Therefore, if you know for sure that you will always have one and only one town linked to a business, you could do something like that:

{% set businessesByTown = businesses|group('bizTown[0].title') %}


If the title field is the name of the town you should get an associative array with the town names as keys and the businesses entries as values.

Additional info about sorting, following swthate's comment below:

If you want to sort the businesses, I think it can be done in the original query, so it would become:

{% set businesses = craft.entries.relatedTo(category).order('title') %}


However, the towns cannot be sorted directly since Twig's sort filter uses asort which sorts the array based on values. What you can do then is extract the businessesByTown array's keys in another array:

{% set towns = businessesByTown|keys|sort %}


You now have a sorted list of towns. Using this list, you can loop on all towns and businesses like that:

{% for town in towns %}
    {{ town }}
    {% set townBusinesses = businessesByTown[town] %}
    {% for business in townBusinesses %}
        {{ business.title }}
    {% endfor %}
{% endfor %}