I am looking to study children's nursing at uni. Is it still possible to apply for a nursing bursary for the army?

You would only be able to apply for an Army Nursing Bursary, if you had a place studying Adult or Mental Health nursing. Upon completion and registration with your NMC pin you would then complete the professionally qualified officer course at Sandhurst. Upon completion you would be an Army Nursing Officer and posted to one of our joint hospital groups.

Are they going to provide bursary only or they do fund full to the nursing course?

You can apply to the Army to become nurse in the Queen Alexandra's Royal Army Nursing Corps (QARANC (QAs for short)), where you would complete your 14 weeks army basic training (with other people also going into the QAs.) before then attending a 3 year nursing degree course at Birmingham City University where, on completion you will be employed in the Army as a Registered Nurse (with the rank of Corporal). You attend the course with a mixture of military and civilian as it is a completely civilian led course (you don't wear army uniform during the course!). Not only is your university degree fully funded, you are also on a good salary (£21,409 per year) and your accommodation (plus gas, electric, water etc) and food is also very heavily subsidised!
You will need 120 UCAS points + 3 GCSEs (Grade A-C (9-4)) in Maths, English and at least a science (Can be double/triple award) or Health and social care. Full entry requirement can be found on the Birmingham City University Website as well as the army website under student nurse (Soldier). I hope this helps.