Praise be to Allaah.
If the University or the body that gives this bursary
stipulates that it should be spent on matters having to do with study, then
he has to adhere to that stipulation and not spend it on anything else, even
if it is for Hajj.
If the body that granted this bursary did not make any such
stipulation; rather it gave it to him because he is a student, then it has
become his property on the basis that he is entitled to it, and he may spend
it on whatever he wants of permissible things or save it for Hajj and take a
student loan to spend on his maintenance.
But that is on condition that this loan is not based on riba
and does not involve paying back more than he took, even if the additional
amount is very small, because that is riba which is haraam.
But we do not advise the questioner to get involved in debt,
even with the aim of doing Hajj; rather it is not permissible for him to get
into this loan in the first place if he does not have the means to pay it
back and does not have any hope of doing so.
If he does hope that he will be able to pay back, there is
nothing wrong with him taking it on, so long as it is free of riba. But it
is better for a person not to take debt upon himself whenever it is possible
to avoid that.
See also the answers to questions no.
And Allah knows best.