Ibrox winger Bedoya netted the opening goal in the 2-0 friendly win over Linfield at Windsor Park in Belfast, the strike coming less than a week after he hit the target for the Light Blues for the first time in the 5-0 SPL win over Dundee United.
And it has made the United States international, who has hardly featured in Ally McCoist's side since moving to Scotland last summer, desperate to stay.
He said: "I try to enjoy myself when I go on to the park, to get the crowd going, give people something to cheer about. I think we managed to do that as a team.
"To get a goal in the second half was the icing on the cake for me. It has definitely been an encouraging few days for me after what has been a very tough few months for everyone at the club.
"This season hasn't gone the way I would've wanted it to. I had a few injuries and couldn't get a place in the team when I managed to regain fitness.
"But in football you have to be patient sometimes and wait for your chance and that is exactly what I have done.
"It may be getting towards the end of the season, but I think I have shown what I can do against Dundee United, Motherwell at the weekend and Linfield yesterday.
"I scored against United and Linfield and I thought I added a bit of spark to the team when I came on against Motherwell – even though I missed a great opportunity."
Bedoya added: "I am in a more positive frame of mind about the future now than I have been at times this season.
"The dressing room has been amazing throughout the whole thing. I would like to come back if everything can get sorted out next season. Of course I would.
"Rangers is a great club and I am proud to be a part of it. I was more than happy to take my wage cut to help the club through this tough time and hopefully we will come through the other side a better club.
"We will see what happens in the summer. It could be busy. But I think the club is here to stay.
"The fans who supported us showed how great they are yesterday, as they have in the last few months."