"Bear a cost" refers to bearing or accepting the financial or non-financial burden of a certain situation or action. Some synonymous phrases for "bear a cost" include "incur expense," which conveys spending money, "pay the price," which implies there may be negative consequences, and "shoulder the burden," which suggests carrying a heavy weight. Other related phrases that could be used are "foot the bill," "absorb the cost," "cover the expenditure," or "carry the weight." Overall, these phrases all communicate the idea of taking responsibility and carrying the consequences of a particular action or decision.