Will one hot encoding / unbalanced columns cause bias to Clustering Analysis?
To answer your question we need to understand what the aim of the clustering analysis that you are doing. Some of goal's of clustering analysis are:


Outlier Detection,
Pattern Detection,
Grouping Data together, etc


Now depending on the type of data, we can choose the algorithm that best fits the data at hand. If you have only numerical features, then you can go for KMeans. If there is a only categorical features we can choose K-Prototypes algorithm and if there is a mix of both categorical and numerical, we can use the K-Medoids algorithm.

To answer your question specifically, we need to choose an appropriate clustering algorithm while using one-hot encoded data to avoid the issues that you are worried about. Since one-hot encoding is intended for categorical features, we have to go with an algorithm that is specifically designed for that. For example K-Prototypes or K-Medoids. 

I would recommend you to understand the exact business problem that you are trying to solve. Correlate that to the data at hand and then use an appropriate mentioned algorithm to solve the problem that you are facing. 

Regards,