The bonding ability between basalt fiber bundle and asphalt mortar has a great influence on the properties of basalt fiber reinforced asphalt mixtures, yet the studies about the bonding between them is very limited. In this paper, a new test instrument called fiber-asphalt pulling machine and a new index called the nominal bonding stress (NBS) were designed and adopted to test and reveal the bonding between basalt fiber bundle and asphalt mortar. The procedures and rationality analysis of this new experiment was specified in this paper. In order to verify the reliability of the NBS index, the NBS values derived from this new test method and the rheological property indexes values of asphalt mortar under different powder–cement ratios were adopted to analyze the correlation between them. Two kinds of basalt fibers produced by two different manufacturers were adopted to conduct the parallel experiment. The results show that the nominal bonding stress between basalt fiber and asphalt mortar derived from this new test has a great correlation with the rheological properties of asphalt mortar, which also proves the credibility of this new test method and the NBS index.