Synonym phrase match

What are your settings for the default operator and the fuzzy search?

The correct format is simply

bed side=bedside

However, depending on what kind of search settings you have, this may not have much effect. If you have OR operator enabled and the synonym set, the search for bed side becomes bed side bedside, which will still match the bed results.

Relevanssi Premium has a feature where you can index synonyms, making it possible to use synonyms with AND search. That might help in this case to reduce the garbage results.

Default operator is AND.

Fuzzy search “When straight search gets no hits”.

I tired disabling OR fallback but this had no effect.

If you have AND enabled, synonyms are simply not used. They are only used in OR searches (unless you have Premium, and enable indexing synonyms).

Here’s one approach:

add_filter('pre_get_posts', 'rlv_word_filter');
function rlv_word_filter($query) {
    $query->query_vars['s'] = str_replace('bed side', 'bedside', $query->query_vars['s']);
}

Add this code to your theme functions.php file. Whenever someone searches for “bed side”, it is automatically transformed into “bedside”. If there are just few problem phrases, this approach works.