Translation:I am not used to eating soup without bread.
Yes, the English "not used to eating..." Is correctly grammatically. When I lived in Russia, I did make some Oriental styled noodle soup for a friend, Alexeii. When I served him a bowl from the pot, he just stared at it. When I asked him what was wrong, he innocently asked with slight puzzlement, "Oh, I am just waiting for the bread."
Привыкал is imperfective aspect. You use this form when you want to describe the process (for example you "were getting used to the hot temperature while living in Africa (a long time - it wasn't immediately)). It also doesn't mean that after that time you are really adapted (maybe you are) but it means that you participated in the process (without knowing the result). On the other hand привык (perfect form) has two meanings: 1) you did adapt to the temperature (and let's say it was quite quick because you just say it happend and you are not discribing how or how long it was happening) (=verb) 2) you ARE used to (adapted to) the temperature (at this moment) (=adjective) I hope it helps. I am not a native speaker myself but in my mother tongue (Czech) it works the same way.
Technically, there is no present form of привык because it is Perfective aspect (привы́кнуть), and there is no present tense for Perfective verbs.
Я привыкаю is the present tense of the Imperfective verb (привыка́ть).
Having said that, I'm not exactly certain how to make a precise distinction here. The exercise appears to be saying "I am not used to [something] NOW because of things that happened in the past".
If you used the Imperfect, the translation would be more like "I am not getting used to eating soup without bread" - whatever that means. It seems like an impossibility that you could be currently not getting used to something - it has to have been a past experience, resulting in a current condition.
Because "to be used to" (as opposed to just "used to" without some form of "to be" in front) cannot be followed by the another verb in the infinitive. It should be followed by either a noun or a gerund instead:
I used to do something
I am used to doing something
"I haven't got used to eating soup without bread" can formally be correct but in reality is unlikely:
"I am not used to ..." simply indicates your current state.
"I haven't got used to ..." means that you tried to get used to but have not (yet) succeeded. In this case we would most likely sat "Я не могу/смог привыкнуть..."="I can/could not get used to..."
Where I'm from, eating soup with bread is considered well nasty and not common. Maybe because we eat mainly soup that is water cooked up with vegetables and spice (noddle soup). Do you, here, mean soup as a stew? Because I don't see anyone eating noodle soup along with bread.