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We consider the space $D(X,Y)$ of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . We show some additional properties of $D(X,Y)$ and investigate the subspace $D^{*}\left(X\right)$ of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence ${\tau }_p$. The largest part of the paper is devoted to the study of various cardinal functions for $(D^{*}\left(X\right),{\tau }_p)$, in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, $\pi$-weight, $\pi$-character,...