If one is unable to ask someone to bring him the water[1] then the following is the ruling: Some Poskim[2] rule one should run to the water in order to hasten the removal of the impurity. Others[3] rule one should walk in a way that he stops[4] every four Amos [6 feet 4 inches] until he reaches the water. Practically one is to follow this latter ruling.[5] However if this will cause one to miss saying Shema on time, then obviously he should run to the water.[6]
[1] Kaf Hachaim 4:2
[2] Shaareiy Teshuvah 1:2; M”B 1:2; Beis Oveid 3; Seemingly however the Shaareiy Teshuvah later retracted this ruling as in his Sefer Mateh Efraim 619:27 in which he rules that one is to walk less than four Amos at a time.[Ketzos Hashulchan 1 supplements page 82]
[3] Birkeiy Yosef 1 as he received from elder Rabbis, brought in Shaareiy Teshuvah 1:2; Morah Baetzba; Kesher Gudal 1:4; Shalmei Tzibur 18; Zechor Liavraham 3; Ruach Chaim 1; Pesech Dvir 1:1; Ben Ish Chaiy Toldos 7; Ketzos Hashulchan 2:1; Mateh Efraim 619:27; Artzos Hachaim 4:3; Misgeres Hashulchan 2; Toras Yekusiel 1; Miasef Lechol Hamachanos 1:9; Bikurei Shlomo [brought in Ketzos Hashulchan 1 supplement p. 82]
[4] It suffices to stand. However some Poskim [Ruach Chaim ibid] rule one is to actually stop and sit. [Kaf Hachaim 4:2]
[5] Ketzos Hashulchan 2:1 as regarding spiritual matters one may not divert from the Kabala. [ibid footnote 6]; Kaf Hachaim 4:2; Even the Shaareiy Teshuvah later retracted this ruling as in his Sefer Mateh Efraim 619:27 he rules that one is to walk less than four Amos at a time.[Ketzos Hashulchan 1 supplements page 82] See Piskeiy Teshuvos 1:7 who rules that within the same room one is to run to the water. Vetzaruch Iyun as the above Poskim do not differentiate and as concludes the Ketzos Hashulchan “we do not move from the words of the Kabalists”.
[6] Ketzos Hashulchan 2 footnote 6