Signing a document involves two steps: (1) hash the document, (2) sign the hash using the private key. The running time is the sum of the running times of each step.
The running time to hash the document will generally be very fast, and depends linearly upon the size of the document. You should expect that a modern computer can hash a document at a rate of about 100-500 MB/sec (megabytes per second). In other words, for a normal size document, this will be done faster than a human can notice. So, for most purposes, you can disregard the time it takes to hash the document, and consequently, in practice, the length of the document usually will be irrelevant.
The running time to sign the document will be heavily dependent upon the size of your RSA key (the number of bits in the modulus). Here are some example timings: computing a signature might take about 1 millisecond for a 1024-bit RSA key; about 5 milliseconds for a 2048-bit RSA key; or about 30 milliseconds for a 4096-bit RSA. (These numbers are only examples and might be somewhat faster or slower depending upon how fast your particular computer is.) Generally, the bulk of the time computing the signature will be spent on the RSA computation, which is very dependent upon the size of the RSA key. Nonetheless, for the key sizes typically used, this is still faster than a human can notice.
So, for reasonable sized documents and reasonable size RSA keys, the signing operation will likely be so fast that you probably won't notice the time it takes to compute the signature.