An in-situ infiltration and reaction (IR) method is one of the most promising methods for the mass production of dense MgB$_{2}$ with a filling factor of over 90%. This is because it does not require an apparatus that applies physical pressure during synthesis, in contrast to the hot isostatic pressing, hot pressing, and spark plasma sintering methods. To promote the infiltration of Mg melt into the B preform, a low-reactivity crystalline B has usually been used to create MgB$_{2}$ bulks with centimetric dimensions. In this paper, we attempted to fabricate large MgB$_{2}$ bulks by the IR method using highly reactive amorphous B, which should result in a high critical current, as reported in the literature. To promote the intrusion of Mg melt, we mixed a small amount of Mg into the amorphous B preform, which is expected to give a similar effect to the so-called premix method. We successfully produced IR-processed MgB$_{2}$ disk bulks, of 20 mm diameter and 5 mm thickness, at a reaction temperature of 700 °C with a holding time of 9 or 24 h. A trapped field $B_\mathrm{T}$ of 1.85 T at 20 K was obtained at the surface centers of the MgB$_{2}$ bulks, which is comparable with the $B_\mathrm{T}$ values of dense MgB$_{2}$ bulks prepared by the hot isostatic pressing, hot pressing, and spark plasma sintering methods. Therefore, we can conclude that the Mg premixing method is an effective way of preparing dense MgB$_{2}$ bulks with a high $B_\mathrm{T}$ by the IR process using amorphous B.