Re: So there is a slug Sage mode, why has it not been shown.?
Hashi mastered it that's why he activates it so quickly. Remember it took naruto a long ass time at first to get into it but now he almost instantly goes into it.
Also, Assuming tsunade has it, she's never had the necessary opportunity to use it. Remember, Tsunade is a medic first, fighter second. SM Isn't really necessary for her to heal people.
Sannin 3 way - Tsunade didn't even need byakugo for that, so SM was extremely unnecessary.
Pain invasion - She was completely occupied with healing the village, and had no reason to go fighting. It's better for her to heal people and have 10k people constantly fighting, than to let those 10k people die just for her(1 person) to fight. The village would have been torn through far easier, and there would have been far more dead bodies. Also, when she finally had an opportunity to go SM -- Pain CST konoha -- she was so exhausted, and so preoccupied that she didn't really have a moment to meditate.
Against madara, she could have entered it before heading off, but the thing is, she probably doesn't have SM. The fact that there's slug SM doesn't mean tsunade needs to have it. Orochimaru couldn't get DSM. Jiraiya couldn't Master FSM. It would be awkward as shit if tsunade just came through with, not only immortality (byakugo), SSM. In any case, I believe byakugo is actually derived from SSM. It's quite possibly a way around the fact she could never collect natural energy, but figured a way to at least get one of the skills of SSM. Hashi is the only other (possible) SSM user we've seen, and it's said he had instantaneous, seal-less healing - just like tsunade - it's possible that only occurs during His Sage mode, so it's a sage mode ability, since he was injured during the last scene with madara.
It'd make more sense if sakura has SM. She at least has a good reason for not using it. Against sasori, she most likely didn't learn it yet since she was still starting her training with sasori. During war - for the same reason she never showed byakugo - she was too pre-occupied healing people and moving around. She never had a chance to sit and meditate. And, that's all assuming she's even mastered it to the point where she can get into it quickly. Remember, it's possible that it might even take her 10 minutes, like jiraiya, to get into; Therefore, she really doesn't have a chance, ATM, to sit and waste 10 minutes to get into SM. Maybe after other kage come and tsunade takes over healing, sakura would have a chance to meditate, because while she's healing right now, she's concentrating too much on transfering chakra to meditate to collect sage chakra. It'd be like looking left and right at the same time - Giving away her chakra and collecting natural chakra at the exact same time.