One search filter always belongs to one custom field, so you cannot merge several separate checkbox fields into a single dropdown. Put the options into one field instead. Create a single multiselect (or select) field whose options are the things you had as separate checkboxes, then add that field to the search.

1. Go to Places > Settings > Custom Fields and add a Multiselect field. Enter each option you need, one per line. Adding Options to GeoDirectory Custom Fields shows the format.
2. In the field settings, set the multiselect display type to checkboxes if you want listing owners to tick the options on the add listing form.
3. Go to Places > Settings > Search (Advanced Search add-on) and add the new field.
4. Turn on Main search bar? for the field and save.

The steps are also in How to Add a Filter to the Main Search Bar?.

The main search bar only has room for one control per field, so a multiselect field shows there as a normal dropdown and visitors pick one option. If visitors need to tick several options at once, leave the field in the advanced filters panel, where it can show as checkboxes. You can set the GD > Search block to show the filters open so they read as part of the search form.

Existing listings keep the values from your old checkbox fields until they are edited, so plan to move that data across before you delete the old fields. A CSV export and import is the quickest way to do that for many listings.