It was worth a try. Besides, he feels like he needs to poke at the Bruceness of Bruce, in the least obtrusive way possible, to get a more complete feel of how he compares to the Bruce he's always known. Not that he realistically expects to get anything like a complete picture.
It is somehow reassuring to know that he still can't cook, though maybe that's an odd universal constant to latch onto (if Bruce can't cook, it means he's never really had to, which means he has Alfred, which means Alfred is the universal constant Tim is really seeking out don't argue with this logic).
Tim does spend a moment or two scanning the apartment and poking into corners, but it's clearly a safe house and bare of anything beyond the basic necesseties. So he heads into the bathroom to clean himself up, splashing cold water in his face and then considering how to tackle his hair. He ends up leaning halfway into the shower and using the showerhead to rinse out the dye while keeping his head tilted down, to avoid getting the rest of him wet, and he will try to make sure it's all out before drying his hair so there aren't any suspicious faint red stains left on Bruce's towels.
It gives him time to think, and he knows he needs to call Conner, or at least send him a message - it's not like at home, where his missions are completely his business unless they involve the Titans or he chooses to call in his friends. He and Conner are stuck here together, essentially alone for the time being, and they need to look out for each other. Even if he does prefer to do things solo... he also doesn't want Conner worrying unduly. A worried Super is nothing to underestimate.
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It is somehow reassuring to know that he still can't cook, though maybe that's an odd universal constant to latch onto (if Bruce can't cook, it means he's never really had to, which means he has Alfred, which means Alfred is the universal constant Tim is really seeking out don't argue with this logic).
Tim does spend a moment or two scanning the apartment and poking into corners, but it's clearly a safe house and bare of anything beyond the basic necesseties. So he heads into the bathroom to clean himself up, splashing cold water in his face and then considering how to tackle his hair. He ends up leaning halfway into the shower and using the showerhead to rinse out the dye while keeping his head tilted down, to avoid getting the rest of him wet, and he will try to make sure it's all out before drying his hair so there aren't any suspicious faint red stains left on Bruce's towels.
It gives him time to think, and he knows he needs to call Conner, or at least send him a message - it's not like at home, where his missions are completely his business unless they involve the Titans or he chooses to call in his friends. He and Conner are stuck here together, essentially alone for the time being, and they need to look out for each other. Even if he does prefer to do things solo... he also doesn't want Conner worrying unduly. A worried Super is nothing to underestimate.