I'm sorry to hear about your highly unsatisfactory life situation, hopefully you get the opportunity to start your own life soon. Now I'm almost a little embarrassed I asked, especially since I don't think the dream has much to do with the specifics of your current life situation.
When I try to analyze a dream it is much easier to me if it is a little longer because then there's a development and more material to work with. I will not try to interpret what this dream "means" because I don't really get a feel of what's going on, but since you came back with an honest answer to my question I feel I should give something back.
If we take a look at the symbols in the dream, first there is the wood. The wood is a common symbol for parts of our inner self that is mostly unconscious, because we don’t know the wood like we know our home town for instance. It is not man made, so it is uncivilized or uncultured part of our self, and animals live here rather than humans, so that which goes here are not under our influence, it is “the other”; it is not a part of ourselves were our consciousness rule, but once again we are unconscious of what’s going on here. So woods are of course a common setting for dreams and often we get lost or meet an animal and so forth.
In this unconscious part of yourself you meet a bear. Since this is a recurring symbol that represents something in you that you are not aware of, I recommend that you do a little “bear work”. Read about bears, go to a zoo and watch them, try to get to know what a bear is. Write a short piece about bears -- what are these animals, really? By a little bear trinket, or another symbol for this work. In this way you can integrate the bear in you consciousness even though you don’t know what it means, but you grow an intuitive relationship with this animal. The wood is a part of yourself, and thus the bear is part of yourself, so you might as well get to know it.
When you have built your own “feel” for the bear, you could go on and read about them in dictionaries of symbols, or even dream dictionaries, and so forth, but I would recommend that you create your own image of the bear first, otherwise you get others’ ideas – and the bear in your dream is yours, not theirs, so you should not let “them” tell you what it is.
The bear is dangerous, just like all unconscious material is potentially dangerous to our ego, because it is the other which is threatening the ego’s dominance; so different unconscious aspects of ourselves are often depicted as dangerous animals. But it is in the same time what the philosophical alchemists called prima materia, that is, that which we have to work with for our inner development. Actually bear, lion and dragon are all recurring symbols (almost interchangeably) as prima materia for these mystics, in their works, so having recurring dreams about a bear is potentially a very good starting point. That’s why I recommend that you work with your bear, though cautiously, because it is stronger than you, obviously.
So the bear is an universal symbol – your grandmother is not. Here you need to switch from working with common ideas to personal ideas. First, your actual relationship with you grandmother is important. Is she a helpful person in real life or not? Would she ignore you in real life or not? Since I don’t know anything about her or your relationship with her, I cannot give you any input. (Except that she can represent a universal aspect, as "the great mother" and so forth, but I will not go down that path now.)
In the dream she is representing something partly unknown. Your hope, your wisdom, a bad or good experience – something like that, if she is not just acting like she would in real life. Write down your associations to “grandmother”, with associations we can describe the contents of a dream image. And then you summarize this in a few words, and then you can ask yourself: In what way is xxx ignoring me, or unable to help me?
Then there’s the bike. I assume that you do not have a driver’s license or that you usually don’t get around by car, because it seems that car and bike are interchangeable in dreams and it often depending on which vehicle one usually uses, or would use if any, it is either in the dream. But here there might also be personal associations that are important, for instance, you may have certain associations to the bike which I don’t know about and which makes this vehicle mean something special for you.
But in any case, the bike is your vehicle. It is the way or the machinery your ego uses to get by in life, or at least in this part of your life. So it is important how well it works, and so forth. From this dream we can see that your means of escape are insufficient. You are a little bit trapped, you cannot get help and you really cannot get away. It’s you and the bear. So you might as well get to know him.
To summarize, there is a certain part of you (an energy, a potentiality) that you are unconscious about that is repeatedly trying to get your attention. You are afraid of it because it is something unknown and it has the potentiality to change you. By working with this dream image, you can establish a intuitive, but yet more conscious relationship with it, and then you will see that your dreams about bears changes, and that you grow from the experience.
So that’s my thoughts in this matter, I hope it is of any help to you. All the best.