The TNI Standards don't require that bacteriological samples be brought in on ice (but it's good practice to do so). The current language is as follows:
1.7.5 Sample Handling
a) Samples that require thermal preservation shall be considered acceptable if the arrival temperature of a representative sample container meets the method or mandated temperature requirement.
i) Samples that are delivered to the laboratory on the same day they are collected may not meet the requirements of Section 1.7.5.a). In these cases, the samples shall be considered acceptable if the samples were received on ice.
ii) If sample analysis is begun within fifteen (15) minutes of collection, thermal preservation is not required.
iii) Thermal preservation is not required in the field if the laboratory receives the sample and either begins the analysis or refrigerates the sample within fifteen (15) minutes of collection.
The presence of ice mitigates that samples may not have cooled to the required temperature, provided they are delivered to the lab on the day of sampling. I don't know of any place that we have defined ice as being wet or blue. From personal experience, blue ice doesn't cool as well as wet ice, so I would use wet ice.
To answer your question, then, my opinion is that either wet ice or blue ice would be acceptable under the language of the TNI Standard.